Emneord:
Matematikk,
Stokastisk Analyse/Finans Forsikring og Risiko,
STORE,
STORM,
STOCONINF,
FINEWSTOCH\; Global South
Publikasjoner

BionNadal, Jocelyne & Di Nunno, Giulia (2020). Fullydynamic riskindifference prices and nogooddeal bounds. SIAM Journal on Financial Mathematics.
ISSN 1945497X.
11(2), s 620 658 . doi: https://doi.org/10.1137/18M120436X

Banos, David; Cordoni, Francesco; Di Nunno, Giulia; Di Persio, Luca & Røse, Elin Engen (2019). Stochastic systems with memory and jumps. Journal of Differential Equations.
ISSN 00220396.
266(9), s 5772 5820 . doi: http://dx.doi.org/10.1016/j.jde.2018.10.052
Fulltekst i vitenarkiv.

Corcuera, José Manuel; Di Nunno, Giulia & Fajardo, Jose (2019). Kyle equilibrium under random price pressure. Decisions in Economics and Finance (DAF).
ISSN 15938883.
42(1), s 77 101 . doi:
10.1007/s10203019002314
Fulltekst i vitenarkiv.
Vis sammendrag
We study the equilibrium in the model proposed by Kyle (Econometrica 53(6):1315–1335, 1985) and extended to the continuoustime setting by Back (Rev Financ Stud 5(3):387–409, 1992). The novelty of this paper is that we consider a framework where the price pressure can be random. We also allow for a random release time of the fundamental value of the asset. This framework includes all the particular Kyle models proposed in the literature. The results enlighten the equilibrium properties shared by all these models and guide the way of finding equilibria in this context.

Di Nunno, Giulia; Fiacco, Andrea & Karlsen, Erik Hove (2019). On the approximation of Lévy driven Volterra processes and their integrals. Journal of Mathematical Analysis and Applications.
ISSN 0022247X.
476(1), s 120 148 . doi:
10.1016/j.jmaa.2019.02.051
Fulltekst i vitenarkiv.
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Volterra processes appear in several applications ranging from turbulence to energy finance where they are used in the modelling of e.g.temperatures and wind and the related financial derivatives. Volterra processes are in general nonsemimartingales and a theory of integration with respect to such processes is in fact not standard. In this work we suggest to construct an approximating sequence of Lévy driven Volterra processes, by perturbation of the kernel function. In this way,one can obtain an approximating sequence of semimartingales. Then we consider fractional integration with respect to Volterra processes as integrators and we study the corresponding approximations of the fractional integrals. We illustrate the approach presenting the specific study of the GammaVolterra processes. Examples and illustrations via simulation are given.

Baños, David; Di Nunno, Giulia; Haferkorn, Hannes Hagen & Proske, Frank Norbert (2018). Stochastic functional differential equations and sensitivity to their initial path, In Elena Celledoni; Giulia Di Nunno; Kurusch EbrahimiFard & Hans MuntheKaas (ed.),
Computation and Combinatorics in Dynamics, Stochastics and Control.
Springer.
ISBN 9783030015923.
2.
s 37
 70

Corcuera, José Manuel & Di Nunno, Giulia (2018). KyleBack's model with a random horizon. International Journal of Theoretical and Applied Finance.
ISSN 02190249.
21(2) . doi:
10.1142/S0219024918500164
Fulltekst i vitenarkiv.

BionNadal, Jocelyne & Di Nunno, Giulia (2017). Fullydynamic riskindifference prices and nogooddeal bounds. arXiv.org.
ISSN 23318422.
Fulltekst i vitenarkiv.
Vis sammendrag
The seller’s riskindifference price evaluation is studied. We propose a dynamic riskindifference pricing criteria derived from a fully dynamic family of risk measures on the L_pspaces for p ∈ [1, ∞]. The concept of fullydynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. The family is then characterised by a double time index. Our framework fits well the study of both short and long term investments. In this dynamic framework we analyse whether the riskindifference pricing criterion actually provides a proper convex price system, for which timeconsistency is guaranteed. It turns out that the analysis is quite delicate and necessitates an adequate setting. This entails the use of capacities and an extension of the whole price system to the Banach spaces derived by the capacity seminorms. Furthermore, we consider the relationship of the fullydynamic risk indifference price with nogooddeal bounds. Recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fullydynamic risk measures so that the corresponding riskindifference prices satisfy the nogood deal bounds. The use of nogooddeal bounds also provides a method to select the risk measures and then construct a proper fullydynamic riskindifference price system in the L_2spaces.

BionNadal, Jocelyne & Di Nunno, Giulia (2017). Representation of convex operators and their static and dynamic sandwich extensions. Journal of Convex Analysis.
ISSN 09446532.
24(4), s 1375 1405

Di Nunno, Giulia & Haferkorn, Hannes Hagen (2017). A maximum principle for meanfield SDEs with time change. Applied Mathematics and Optimization.
ISSN 00954616.
76(1), s 137 176 . doi:
10.1007/s0024501794260
Fulltekst i vitenarkiv.

Di Nunno, Giulia & Vives, Josep (2017). A MalliavinSkorohod calculus in L^0 and L^1 for additive and Volterratype processes. Stochastics: An International Journal of Probability and Stochastic Processes.
ISSN 17442508.
89(1), s 142 170 . doi:
10.1080/17442508.2016.1140767
Fulltekst i vitenarkiv.
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In this paper we develop a Malliavin–Skorohod type calculus for additive processes in the L1 and L1 settings, extending the probabilistic interpretation of the Malliavin–Skorohod operators to this context. We prove calculus rules and obtain a generalization of the Clark–Hausmann–Ocone formula for random variables in L1. Our theory is then applied to extend the stochastic integration with respect to volatility modulated Lévydriven Volterra processes recently introduced in the literature. Our work yields to substantially weaker conditions that permit to cover integration with respect to e.g. Volterra processes driven by alfastable processes with alfa < 2. The presentation focuses on jump type processes.

Di Nunno, Giulia & Karlsen, Erik Hove (2016). Hedging under worstcasescenario in a market driven by timechanged Lévy noises, In Mark Podolskij; Robert Stelzer; Steen Thorbjørnsen & Almut E. D. Veraart (ed.),
The Fascination of Probability, Statistics and their Applications. In honour of Ole E. BarndorffNielsen.
Springer Science+Business Media B.V..
ISBN 9783319258249.
Chapter 22.
s 465
 499
Vis sammendrag
In an incomplete market driven by timechanged Lévy noises we consider the problem of hedging a financial position coupled with the underlying risk of model uncertainty. Then we study hedging under worstcasescenario. The proposed strategies are not necessarily selffinancing and include the interplay of a cost process to achieve the perfect hedge at the end of the time horizon. The hedging problem is tackled in the framework of stochastic differential games and it is treated via backward stochastic differential equations. Two different information flows are considered and the solutions compared.

Di Nunno, Giulia; Mishura, Yuliya & Ralchenko, Kostiantyn (2016). Fractional calculus and pathwise integration for Volterra processes driven by Lévy and martingale noise. Fractional Calculus and Applied Analysis.
ISSN 13110454.
19(6), s 1356 1392 . doi:
10.1515/fca20160071
Vis sammendrag
We introduce a pathwise integration for Volterra processes driven by Lévy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they constitute a very flexible class of models, which include fractional Brownian and Lévy motions and it is part of the socalled ambit fields. A pathwise integration with respect of such Volterra processes aims at producing a framework where modelling is easily understandable from an information perspective. The techniques used are based on fractional calculus and in this there is a bridging of the stochastic and deterministic techniques. The present paper aims at setting the basis for a framework in which further computational rules can be devised. Our results are general in the choice of driving noise. Additionally we propose some further details in the relevant context subordinated Wiener processes.

Di Nunno, Giulia & Zhang, Tusheng (2016). Approximations of stochastic partial differential equations. The Annals of Applied Probability.
ISSN 10505164.
26(3), s 1443 1466 . doi:
10.1214/15AAP1122

Benth, Fred Espen; Di Nunno, Giulia; Khedher, Asma & Schmeck, Maren Diane (2015). Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk. Applied Mathematical Finance.
ISSN 1350486X.
22(1), s 28 62 . doi:
10.1080/1350486X.2014.948708

Di Nunno, Giulia & Karlsen, Erik Hove (2015). Hedging under worstcasescenario in a market driven by timechanged Lévy noises. Preprint series (Universitetet i Oslo. Matematisk institutt).
ISSN 08062439.

Di Nunno, Giulia; Khedher, Asma & Vanmaele, Michèle (2015). Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps. Applied Mathematics and Optimization.
ISSN 00954616.
72(3), s 353 389 . doi:
10.1007/s002450149283z

Di Nunno, Giulia & Vives, Josep (2015). A MalliavinSkorohod calculus in L^0 and L^1 for additive and Volterratype processes. Preprint series (Universitetet i Oslo. Matematisk institutt).
ISSN 08062439.

BionNadal, Jocelyne & Di Nunno, Giulia (2014). Representation of convex operators and their static and dynamic sandwich extension. Preprint series (Universitetet i Oslo. Matematisk institutt).
ISSN 08062439.
(4) Fulltekst i vitenarkiv.

Corcuera, Jose Manuel; Di Nunno, Giulia; Farkas, Gergely & Øksendal, Bernt (2014). A continuous auction model with insiders and random time of information release. Preprint series (Universitetet i Oslo. Matematisk institutt).
ISSN 08062439.
(3) Fulltekst i vitenarkiv.

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2014). BSDEs driven by timechanged Lévy noises and optimal control. Stochastic Processes and their Applications.
ISSN 03044149.
124(4), s 1679 1709 . doi:
10.1016/j.spa.2013.12.010

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2014). Information and optimal investment in defaultable assets. International Journal of Theoretical and Applied Finance.
ISSN 02190249.
17(8) . doi:
10.1142/S0219024914500502

Di Nunno, Giulia & Zhang, Tusheng (2014). Approximations of Stochastic Partial Differential Equations. Preprint series (Universitetet i Oslo. Matematisk institutt).
ISSN 08062439.
(1) Fulltekst i vitenarkiv.

Benth, Fred Espen; Di Nunno, Giulia & Khedher, Asma (2013). A note on convergence of option prices and their Greeks for Lévy models. Stochastics: An International Journal of Probability and Stochastic Processes.
ISSN 17442508.
85(6), s 1015 1039 . doi:
10.1080/17442508.2012.736994

Di Nunno, Giulia & BionNadal, Jocelyne (2013). Dynamic nogooddeal pricing measures and extension theorems for linear operators on Linfinity. Finance and Stochastics.
ISSN 09492984.
17(3), s 587 613 . doi:
10.1007/s007800120195y

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2013). On Chaos Representation and Orthogonal Polynomials for the Doubly Stochastic Poisson Process, In
Seminar on Stochastic Analysis, Random Fields and Applications VII.
Birkhäuser Verlag.
ISBN 9783034805452.
Del 1  kap 2.
s 23
 54

Benth, Fred Espen; Di Nunno, Giulia & Khedher, Asma (2012). Computation of Greeks in multifactor models with applications to power and commodity markets. Journal of Energy Markets.
ISSN 17563607.
5(4), s 3 31
Se alle arbeider i Cristin

Celledoni, Elena; Di Nunno, Giulia; EbrahimiFard, Kurusch & MuntheKaas, Hans (ed.) (2018). Computation and Combinatorics in Dynamics, Stochastics and Control.
Springer.
ISBN 9783030015923.
737 s.
Vis sammendrag
The Abel Symposia volume at hand contains a collection of highquality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 1619 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Benth, Fred Espen & Di Nunno, Giulia (ed.) (2016). Stochastics of Environmental and Financial Economics.
Springer Science+Business Media B.V..
ISBN 9783319234243.
360 s.
Se alle arbeider i Cristin

Di Nunno, Giulia (2020). Work in Research in Norway and Scandinavia.

Di Nunno, Giulia; Arici, Francesca & Cherubini, Anna Maria (2020, 02. juli). Going beyond the boundaries: An interview with Giulia Di Nunno. [Internett].
European Women in Mathematics.

Di Nunno, Giulia & Isaksen, Karoline Kvellestad (2020, 31. august). Alumni Spotlight: Giulia Di Nunno. [Internett].
Newsletter CAS Oslo.

Di Nunno, Giulia (2019). Excursus on time change in stochastic analysis and control.

Di Nunno, Giulia (2019, 17. juli). ICIAM 2019 Su Buchin  Prize Prof. Giulia di Nunno. [TV].
WebsEdgeEducation.

Di Nunno, Giulia (2019). Martingale random fields in time change models, the role of information in optimal portfolio problems.

Di Nunno, Giulia (2019). Mathematics, Society, Economy and Development.

Di Nunno, Giulia (2019). Optimal strategies in a market with memory.
Vis sammendrag
We consider a market model driven by Volterra type dynamics driven by a timechanged Levy noise. These dynamics allow both for memory features and clustering effects in the trading times. In this framework, we study an optimal portfolio problem, which is then tackled via maximum principle. To produce such results we use different kind of information flows that take care of the timechange in adequate way and we rely on the nonanticipating stochastic derivative for random fields. Moreover, we study the solutions of Volterra type SDEs and Volterra type BSDEs driven by timechanged Levy noises. Talk based on joint work with Michele Giordano, UiO.

Di Nunno, Giulia (2019). Timechange in modelling, stochastic calculus and control.
Vis sammendrag
Time change is a powerful technique for generating noises and providing flexible models. Its main idea stands in the representation of complicated stochastic structures by some known processes and a randomly perturbed time line. We shall provide an excursus through related stochastic calculus, chaos structure and information, integral representations and stochastic differentiation. These will then be applied to backward stochastic differential equations and optimal control problems. Motivation of our work is taken from stochastic finance.

Di Nunno, Giulia & Natalini, Roberto (2019, 01. august). Interview by Roberto Natalini with Giulia Di Nunno, 2019 Su Buchin Prize Winner. [Internett].
DIANOIA.

Di Nunno, Giulia & Salomon, Mónica G. (2019, 27. august). Hay matemáticos de primer nivel trabajando a destajo en África.
El Pais.

Di Nunno, Giulia (2018). A continuous auction model with insiders and random time of information release.
Vis sammendrag
In a unified framework we study equilibrium in the presence of an insider having information on the signal of the firm value, which is naturally connected to the fundamental price of the firm related asset. The fundamental value itself is announced at a future random (stopping) time. We consider two cases. First when the release time of information is known to the insider and then when it is unknown also to her. Allowing for very general dynamics, we study the structure of the insider’s optimal strategies in equilibrium and we discuss market efficiency. In particular, we show that in the case the insider knows the information release time, the market is fully efficient. In the case the insider does not know this random time, we see that there is an equilibrium with no full efficiency, but where the sensitivity of prices is decreasing in time according with the probability that the announcement time is greater than the current time. In other words, the prices become more and more stable as the announcement approaches. This is joint work with Jose Manuel Corcuera, Gergely Farkas, Bernt Øksendal

Di Nunno, Giulia (2018). Fully dynamic riskindifference pricing and nogooddeal bounds.
Vis sammendrag
In an incomplete market with no a priori assumption on the underlying price dynamics, we focus on the problem of derivative pricing from the seller's perspective. We consider risk indifference pricing as an alternative to the classical utility indifference, so that the actual evaluations are done via risk measures. In addition we propose a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fullydynamic risk measure which extends the one of dynamic risk measure by adding the actual possibility of changing the risk perspectives over time. This entails an analysis on the questions of timeconsistency in the risk and then the price evaluations. The framework proposed fits well the study of both short and long term investments. In this framework we study whether the risk indifference criterion actually provides a proper convex price system. We shall see that some conditions have to be fulfilled. Then we consider the relationship of fully dynamic riskindifference price with nogooddeal bounds. We recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fully dynamic risk measure so that the corresponding riskindifference prices satisfy the nogooddeal bounds. In this way nogooddeal bounds provide a way to select the risk measures to obtain a proper fullydynamic riskindifference price system. The presentation is based on various joint works with Jocelyne BionNadal.

Di Nunno, Giulia (2018). Integration with respect to Levy driven Volterra processes.
Vis sammendrag
Volterra processes appear in several applications ranging from turbulence to energy finance and biological modelling. Volterra processes are in general nonsemimartingales and a theory of integration with respect to such processes is in fact not standard. We present some recent results within the framework of fractional calculus and Malliavin Calculus. As illustration we consider specifically the socalled GammaVolterra processes. The presentation is based on joint works with: Andrea Fiacco, Erik H. Karlsen and Josep Vives.

Di Nunno, Giulia (2018). KyleBacks equilibrium model with a random time of information release.
Vis sammendrag
We consider the continuoustime version of KyleBack’s model, originally from 1985 and 1992. In Back’s model there is asymmetric information in the market in the sense that there is an insider having information on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. The market makers give prices via a pricing rule, that depends on the total demand and a certain price pressure. In this work we consider both the case of deterministic and stochastic price pressure. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. The presentation is based on joint works with: José Manuel Corcuera (U. Barcelona) and José Fajardo (Brazilian School of Public and Business Administration).

Di Nunno, Giulia (2018). KyleBacks equilibrium model with a random time of information release.
Vis sammendrag
The continuoustime version of Kyle (1985)) developed by Back (1992)) is here studied. In Back’s model there is asymmetric information in the market in the sense that there is an insider having infor mation on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium. The talk is based on joint works with: Jose Manuel Corcuera, Bernt Øksendal, Gergely Farkas

Di Nunno, Giulia (2018). KyleBack’s model with a random horizon.
Vis sammendrag
The continuoustime version of Kyle (1985)) developed by Back (1992)) is here studied. In Back’s model there is asymmetric information in the market in the sense that there is an insider having infor mation on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium.

Di Nunno, Giulia (2018). Levy driven Volterra processes: approximation and integration.
Vis sammendrag
Volterra type processes appear in several applications ranging from turbulence, to energy finance, and biological modelling. In general, these processes are not semimartingales and a theory of stochastic integration with respect to such processes is in fact not standard. In this presentation, we consider L\’evy driven Volterra processes and we discuss some recent approaches based on fractional calculus. We study both semimartingale approximations to the Volterra process and approximation to the integral. As illustration, we detail the study of the socalled GammaVolterra processes, which is particularly popular in modelling. This is based on joint works with Andrea Fiacco, Erik Karlsen, Yuliya Mishura, Kostia Ralchenko

Di Nunno, Giulia (2018). Malliavin Calculus and Applications to Finance.

Di Nunno, Giulia (2018). On fullydynamic riskindifference pricing: timeconsistency and other properties.
Vis sammendrag
Riskindifference pricing is proposed as an alternative to utility indifference pricing, where a risk measure is used instead of a utility based preference. In this, we propose to include the possibility to change the attitude to risk evaluation as time progresses. This is particularly reasonable for long term investments and strategies. Then we introduce a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. The riskindifference pricing system is studied from the point of view of its properties as a convex price system. We tackle questions of timeconsistency in the risk evaluation and the corresponding prices. This analysis provides a new insight also to timeconsistency for ordinary dynamic riskmeasures. Our techniques and results are set in the representation and extension theorems for convex operators. We shall argue and finally provide a setting in which fullydynamic riskindifference pricing is a well set convex price system. The presentation is based on joint works with Jocelyne BionNadal.

Di Nunno, Giulia (2018). On the integration with respect to Volterra processes: fractional calculus and approximation.

Di Nunno, Giulia (2018). On the integration with respect to Volterra type processes.
Vis sammendrag
Volterra processes appear in several applications ranging from turbulence, to energy finance, and biological modelling. Volterra processes are in general nonsemimartingales and a theory of integration with respect to such processes is in fact not standard. We consider L\’evy driven Volterra processes and we discuss some some recent approaches and results within the framework of Malliavin calculus and fractional calculus. As illustration we consider specifically the socalled GammaVolterra processes, which is particularly popular in modelling. This is based on joint works with Andrea Fiacco, Erik Karlsen, Yuliya Mishura, Kostia Ralchenko, Josep Vives

Di Nunno, Giulia (2018). Sandwich extensions of linear and convex operators and their applications.
Vis sammendrag
We propose some extension theorems for linear and convex operators from $L_p$ spaces to $L_p$ spaces that preserve both minoring and majoring stochastic bounds. We shall see how these extension theorems are applied within the context of pricing in mathematical finance. We discuss in fact the concept of a pricing system, which is in fact a family of such operators that has to preserve some reasonable conditions, including the timeconsistency to guarantee that the fundamental economic criteria of the nonarbitrage principle is maintained. Various properties and form of pricing operators are presented. This talk is based on a series of works with various coauthors: Sergio Albeverio (U. Bonn), Jocelyne BionNadal (CNRS Ecole Polytechnique), Inga B. Eide (now at Finanstilsynet), Yuri Rozanov (CNR Milano).

Di Nunno, Giulia (2018). Stochastic calculus and control for systems driven by timechanged Levy noises.

Di Nunno, Giulia (2018). Stochastic systems with memory, robustness and sensitivity.
Vis sammendrag
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures. We study the case when the driving noises admit jumps provid ing results on existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. In the case of Brownian driving noise, we consider evaluations based on these models (e.g. the prices of some financial products) and the risks connected to the choice of these models. In particular we focus on the impact of the initial condition on the evaluations. This problem is known as the analysis of sensitivity to the initial condition and, in the terminology of finance, it is referred to as the Delta. In this work the initial condition is represented by the relevant past history of the stochastic functional differential equation. This naturally leads to the redesign of the definition of Delta. We suggest to define it as a functional directional derivative, this is a natural choice. For this we study a repre sentation formula which allows for its computation without requiring that the evaluation functional is differentiable. This feature is particularly relevant for applications. Our techniques make use of stochastic calculus via regularisations, Malliavin/Skorohod calculus and functional derivatives. The presentation is based on joint works with: D.R. Banos, F. Cordoni, L. Di Persio, H.H. Haferkorn, F. Proske, E.E. Røse.

Di Nunno, Giulia (2017). Control of an economic with specialised sectors: a maximum principle approach for meanfield SDEs with time change.
Vis sammendrag
We consider an economy with specialised sectors modelled by a mean eld SDE driven by time change Levy noises. Time change is a powerful technique for generating noises and providing exible models. In this study we fo cus on time changed Brownian and Poisson ran dom measures. We study the existence and uniqueness of the solution to a general mean eld SDEs. Moreover we consider a mean field stochastic control problem for mean field controlled dynamics. In the application this corresponds to a centralised control for the economy under consideration. We present a necessary and sufficient maximum principle to solve the optimal control problem. For this we study existence and uniqueness of solutions to mean field BSDEs in the context of time change. This is based on joint work with Hannes Haferkorn

Di Nunno, Giulia (2017). Dynamic risk indifference pricing.
Vis sammendrag
We deal with dynamic pricing from the seller's perspective in an incomplete market and we focus on risk indifference pricing. We propose a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fullydynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. Our framework fits well the study of both short and long term investments. In the dynamic framework we analyse whether the risk indifference criterion actually provides a proper convex price system. Furthermore, we consider the relationship of the fullydynamic riskindifference price with nogooddeal bounds. Recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fullydynamic risk measure so that the corresponding riskindifference prices satisfy the nogooddeal bounds. As it turns out, nogooddeal bounds also provide a method to select the risk measures that provide a proper fullydynamic riskindifference price system. The presentation is based on joint works with Jocelyne BionNadal.

Di Nunno, Giulia (2017). Dynamic risk indifference pricing.
Vis sammendrag
We deal with dynamic pricing of financial products in an incomplete market and we focus on risk indifference pricing. This can be seen as an alternative to the classical utility indifference pricing in which the performance is written in terms of evaluation of risks instead of utility. We propose a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fullydynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the perspective on how to measure risk over time. Our framework fits well the study of both short and long term investments. Risk indifference pricing has been studied in the terms of how to find a solution and express the actual price under different assumptions on the underlying dynamics and information flows. Typically the price is evaluated at time of the initial investment t=0. We are interested in studying the pricing criterion in its time evolution in a setting free from specific choices of underlying dynamics. In the dynamic framework we analyse whether the risk indifference criterion actually provides a proper convex price system. Furthermore, we consider the relationship of the fullydynamic riskindifference price with nogooddeal bounds. Recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fullydynamic risk measure so that the corresponding riskindifference prices satisfy the nogooddeal bounds. As it turns out, nogooddeal bounds also provide a method to select the risk measures that provide a proper fullydynamic riskindifference price system. The presentation is based on joint works with Jocelyne BionNadal.

Di Nunno, Giulia (2017). Fullydynamic risk indifference pricing.
Vis sammendrag
We deal with dynamic pricing of financial products in an incomplete market and we focus on riskindifference pricing. This can be seen as an alternative to the classical utilityindifference pricing in which the performance is written in terms of evaluation of risks instead of utility. We propose a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fullydynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the perspective on how to measure risk over time. Our framework fits well the study of both short and long term investments. Riskindifference pricing has been studied from the point of view of how to find a solution under different assumptions on the underlying dynamics and information flows. Typically the price is also evaluated at the time of the initial investment t=0. We are interested in studying the riskindifference pricing criterion in its time evolution in a setting free from specific choices of underlying dynamics. In the dynamic framework we analyse whether the riskindifference criterion actually provides a proper convex price system. Furthermore, we consider the relationship of the fullydynamic riskindifference price with nogooddeal bounds. Recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fullydynamic risk measure so that the corresponding riskindifference prices satisfy the nogooddeal bounds. As it turns out, nogooddeal bounds also provide a method to select the risk measures that provide a proper fullydynamic riskindifference price system. Based on joint work with Jocelyne BionNadal

Di Nunno, Giulia (2017). Fullydynamic riskindifference pricing with nogooddeal bounds.
Vis sammendrag
We deal with the pricing of claims in an incomplete market and we focus on riskindifference pricing techniques. We propose a fullydynamic riskindifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fullydynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. In this talk we shall explain what riskindifference pricing is, convex risk measures and how these are going to be used. We shall use techniques of functional analysis mixed with probability theory to study these price operators and see if they fulfill the criteria to be proper convex prices. We restrict the presentation to the L2framework where we can exploit the dynamic nogood deal bounds to obtain a complete characterization of these dynamic prices. We shall recall that nogooddeal prices are those prices that guarantee that in the market there are no arbitrage opportunities and there are ”no deals that are too good to be true”. The presentation is based on joint works with Jocelyne BionNadal

Di Nunno, Giulia (2017). Introduction to Levy Processes and Applications to Finance.

Di Nunno, Giulia (2017). Malliavin Calculus for Lévy processes and TimeChange.

Di Nunno, Giulia (2017). Mathematics, Modelling, Time and Chaos.

Di Nunno, Giulia (2017). On the integration with respect to Volterra processes: fractional calculus and approximation.
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In the first part we discuss a pathwise integration for Volterra processes driven by L\'evy noise or martingale noise based on fractional calculus. We obtain an integral with respect to a nonsemimartingale process. Different from other recent approaches, this integration provides a framework for modelling where it is easy to keep track of the information flow. Then it can be attractive for applications, for example in finance and energy finance, where information is often linked to portfolio management and control. Then we study an approximation of the integrals introduced above based on the perturbation of the noise, which provides a semimartingale approximation of the integral. This turns to be interesting for simulations. This is based on joint work with Yuliya Mishura, Kostia Ralchenko, Erik H. Karlsen

Di Nunno, Giulia & Isaksen, Karoline Kvellestad (2017, 08. mars). Det er vanskeligere for kvinner å komme seg opp og fram i matematikken. Intervju til: Professor Berit Stensønes (CAS gruppeleder 2016/17, NTNU), Professor Giulia Di Nunno (CAS gruppeleder 2014/15, UiO), Professor Knut Liestøl (Styreleder for Forskningsrådet BALANSE project, UiO), Professor Geir Ellingsrud (CAS Styreleder, UiO).
Forskning.no.

Di Nunno, Giulia (2016). A MalliavinSkorohod calculus in L^0 and L^1 for additive and Volterratype processes.

Di Nunno, Giulia (2016). Risk indifference pricing and dynamic nogooddeal bounds.

Di Nunno, Giulia (2016). Sensitivity analysis in a market with memory. A join work with D.R.Banos, H.Haferkorn, f. Proske.

Di Nunno, Giulia (2016). Sensitivity analysis in a market with memory. Work in collaboration with D.R. Banos, H. Haferkorn, F. Proske..

Di Nunno, Giulia (2016). Series of Lectures on Levy Processes and Applications to Finance.

Di Nunno, Giulia (2016). Stochastic systems with memory and jumps.

Di Nunno, Giulia (2015). Dynamic no good deal bounds: linear and convex price systems.

Di Nunno, Giulia (2015). Dynamic no good deal bounds: linear and convex price systems.

Di Nunno, Giulia (2015). Intensive course: Malliavin Calculus for Levy Processes.

Aarønæs, Lars; Benth, Fred Espen & Di Nunno, Giulia (2014, 01. oktober). Hvordan beregner vi framtida?. [Tidsskrift].
GLIMT  CAS Informasjonsblad.

Di Nunno, Giulia (2014). A continuous auction model with insiders.

Di Nunno, Giulia (2014). A continuous auction model with insiders and information release.

Di Nunno, Giulia (2014). Optimal portfolio problems with price dynamics driven by timechanged Levy noises.

Di Nunno, Giulia (2014). Optimal portfolios in markets driven by timechanged Levy noises.

Di Nunno, Giulia (2014). Timechanged Levy processes and hedging formulae.

Di Nunno, Giulia (2013). BSDEs driven by timechanged Levy noises and optimal control. Based on joint work with Steffen Sjursen.

Di Nunno, Giulia (2013). BSDEs driven by timechanged Levy noises and optimal control.Based on joint work with Steffen Sjursen.

Di Nunno, Giulia (2013). Backward stochastic differential equations with applications to dynamic risk measures. Series of 5 lectures.

Di Nunno, Giulia (2013). Introduction to stochastic calculus and stochastic differential equations. Series of 8 lectures.

Di Nunno, Giulia (2013). Market with memory: pricing and sensitivity analysis. Based on joint work with Frank Proske and David Banos.

Di Nunno, Giulia (2013). Quadratic Hedging via Backward Stochastic Differential Equations with Jumps. Based on joint work with Asma Khedher and Michele Vanmaele.

Di Nunno, Giulia (2013). Robustness of BSDEs and applications to quadratic hedging. Based on joint work with Asma Khedher and Michele Vanmaele.

Di Nunno, Giulia (2013). Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps. Based on joint work with Asma Khedher and Michele Vanmaele.

Di Nunno, Giulia (2013). Robustness of quadratic hedging strategies to model risk. Based on joint work with Asma Khedher and Michele Vanmaele.

Di Nunno, Giulia; Khedher, Asma & Vanmaele, Michèle (2013). Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps. Preprint series: Pure mathematics. 9. Fulltekst i vitenarkiv.

Sjursen, Steffen A. Søreide & Di Nunno, Giulia (2013). BSDES DRIVEN BY TIMECHANGED LEVY NOISES AND OPTIMAL CONTROL. Preprint series (Universitetet i Oslo. Matematisk institutt). 1. Fulltekst i vitenarkiv.

Benth, Fred Espen; Di Nunno, Giulia; Khedher, Asma & Schmeck, Maren Diane (2012). Pricing of spread options on a bivariate jump market and stability to model risk. Preprint series (Universitetet i Oslo. Matematisk institutt). 2. Fulltekst i vitenarkiv.

Benth, Fred Espen; Di Nunno, Giulia; Khedher, Asma & Schmeck, Maren Diane (2012). Spread options and stability to model risk.

Di Nunno, Giulia (2012). Aspects of Malliavin Calculus.

Di Nunno, Giulia (2012). Sensitivity analysis and computation of the Greeks.

Di Nunno, Giulia & BionNadal, Jocelyne (2012). Dynamic no good deal bounds and pricing measures.

Di Nunno, Giulia & BionNadal, Jocelyne (2012). Dynamic no good deal pricing measures.

Di Nunno, Giulia; L'Aurora, Edoardo; Moschetta, Marina; Proske, Frank Norbert & RuizBanos, David (2012). Market with memory and sensitivity to the past.

Di Nunno, Giulia; L'Aurora, Edoardo; Moschetta, Marina; Proske, Frank Norbert & RuizBanos, David (2012). Market with memory: pricing and sensitivity analysis.

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2012). Doubly stochastic Poisson random fields: from integral representations to BSDEs.

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2012). Integral representations and BSDEs driven by doubly stochastic Poisson processes.

Di Nunno, Giulia & Sjursen, Steffen A. Søreide (2012). On chaos representation and orthogonal polynomials for the doubly stochastic Poisson process. Preprint series (Universitetet i Oslo. Matematisk institutt). 1. Fulltekst i vitenarkiv.
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Publisert 13. nov. 2010 13:11
 Sist endret 8. mai 2020 09:54