-
Di Nunno, Giulia
(2023).
On stochastic control for time changed Lévy dynamics.
-
Di Nunno, Giulia
(2023).
Horizon risk and fully dynamic risk measures.
-
Di Nunno, Giulia
(2023).
Pricing in sandwiched Volterra volatility models.
-
Di Nunno, Giulia
(2023).
Dynamic risk assessment, horizon risk, and interest rate uncertainty.
-
Di Nunno, Giulia
(2023).
Sandwiched Volterra volatility models and hedging.
-
Di Nunno, Giulia
(2023).
Sandwiched Volterra volatility models and hedging.
-
Di Nunno, Giulia
(2023).
Sandwiched Volterra volatility models and hedging.
-
Di Nunno, Giulia
(2023).
Optimal control for Volterra type dynamics.
-
Di Nunno, Giulia
(2023).
Sandwiched Volterra volatility models and option pricing.
-
Di Nunno, Giulia
(2023).
Lifting of Volterra processes: Optimal control in UMD Banach spaces
.
-
Di Nunno, Giulia
(2023).
Research on Risk Measures.
-
Di Nunno, Giulia
(2023).
Horizon risk and dynamic risk assessment.
-
Di Nunno, Giulia
(2023).
Horizon risk and fully dynamic risk measures.
-
Di Nunno, Giulia; Natalini, Roberto & Luca, Perri
(2022).
La matematica unisce.
[Internett].
https://www.youtube.com/watch?v=-Sj-3w0GXvw.
-
Di Nunno, Giulia
(2022).
Fully-dynamic risk measures and horizon risk.
-
Di Nunno, Giulia
(2022).
Stochastic games
for Volterra time-changed Lévy dynamics.
-
Di Nunno, Giulia
(2022).
On time changed Lévy noises
in modelling, dynamics and control
.
-
Di Nunno, Giulia
(2022).
Stochastic games
for Volterra time-changed Lévy dynamics.
-
Di Nunno, Giulia
(2022).
Sandwiched SDEs with unbounded drift,
Hölder noises and stochastic volatility modelling.
-
Di Nunno, Giulia
(2022).
Horizon risk and fully-dynamic risk measures.
-
Di Nunno, Giulia
(2022).
Optimal control of Volterra type equations: from finite to infinite dimensions and return.
-
Di Nunno, Giulia
(2022).
Fully-dynamic risk measures: time-consistency, horizon risk, and relations with BSDEs and BSVIEs.
-
Di Nunno, Giulia
(2022).
Stochastic games
for Volterra time-changed Lévy dynamics.
-
Di Nunno, Giulia
(2022).
Sandwiched SDEs with unbounded drift driven by Hölder noises.
-
Di Nunno, Giulia
(2021).
Maximum principles for stochastic time-changed Volterra games.
-
Di Nunno, Giulia
(2021).
Sensitivity analysis in the infinite dimensional Heston model.
-
Di Nunno, Giulia
(2021).
Infinite dimensional Heston model and sensitivity analysis.
-
Di Nunno, Giulia
(2021).
Rough volatility: SDE with unbounded drift driven by Hölder continuous noise.
-
Di Nunno, Giulia
(2021).
Sensitivity analysis in the infinite dimensional Heston model.
-
Di Nunno, Giulia
(2021).
Optimal portfolios in markets with memory.
-
-
Nunno, Giulia Di
(2021).
On time changed Lévy noises in modelling, dynamics and control.
-
Nunno, Giulia Di
(2021).
Maximum principles for stochastic time-changed Volterra games.
-
Nunno, Giulia Di
(2021).
Sensitivity analysis in the infinite dimensional Heston model.
-
Nunno, Giulia Di; Benth, Fred Espen & Simonsen, Iben Cathrine
(2021).
Infinite dimensional Heston model and sensitivity analysis.
-
Nunno, Giulia Di & Yurchenko-Tytarenko, Anton
(2021).
Rough volatility: SDE with unbounded drift driven by Hölder continuous noise.
-
Nunno, Giulia Di
(2021).
Sensitivity analysis in the infinite dimensional Heston model.
-
Nunno, Giulia Di
(2021).
Optimal portfolios in markets with memory.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2021).
Volterra Sandwiched Volatility Model.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2021).
Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2021).
Volterra Sandwiched Volatility Model.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2021).
Volterra Sandwiched Volatility Model.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2021).
Stochastic volatility modelling via sandwiched processes with Volterra noise.
-
Di Nunno, Giulia
(2020).
Infinite dimensional Heston model: pricing and sensitivity analysis
.
-
Di Nunno, Giulia
(2020).
Stochastic control for Volterra equations driven by time-changed noises
.
-
Di Nunno, Giulia
(2020).
Stochastic control for Volterra equations driven by time-changed noises
.
-
Di Nunno, Giulia
(2020).
Stochastic control for Volterra equations driven by time-changed noises.
-
Nunno, Giulia Di
(2020).
Infiite dimensional Heston model: pricing and sensitivity analysis.
-
Nunno, Giulia Di
(2020).
Stochastic control for Volterra equations driven by time-changed noises
.
-
Nunno, Giulia Di
(2020).
Stochastic control for Volterra equations driven by time-changed noises.
-
Nunno, Giulia Di
(2020).
Stochastic control for Volterra equations driven by time-changed noises.
-
Giordano, Michele & Nunno, Giulia Di
(2020).
Lifting of Volterra processes: optimal control and HJB equations.
-
Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton
(2020).
Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
-
Di Nunno, Giulia; Arici, Francesca & Cherubini, Anna Maria
(2020).
Going beyond the boundaries: An interview with Giulia Di Nunno.
[Internett].
European Women in Mathematics.
-
Di Nunno, Giulia & Isaksen, Karoline Kvellestad
(2020).
Alumni Spotlight: Giulia Di Nunno.
[Internett].
Newsletter CAS Oslo.
-
Di Nunno, Giulia
(2020).
Work in Research in Norway and Scandinavia.
-
Di Nunno, Giulia
(2019).
Excursus on time change in stochastic analysis and control.
-
-
-
-
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 time-changed 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 time-change in adequate way and we rely on the non-anticipating stochastic derivative for random fields. Moreover, we study the solutions of Volterra type SDEs and Volterra type BSDEs driven by time-changed Levy noises.
Talk based on joint work with Michele Giordano, UiO.
-
Di Nunno, Giulia
(2019).
Time-change 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
(2019).
Martingale random fields in time change models, the role of information in optimal portfolio problems.
-
Di Nunno, Giulia
(2018).
On fully-dynamic risk-indifference pricing: time-consistency and other properties.
Vis sammendrag
Risk-indifference 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 fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. The risk-indifference pricing system is studied from the point of view of its properties as a convex price system. We tackle questions of time-consistency in the risk evaluation and the corresponding prices. This analysis provides a new insight also to time-consistency for ordinary dynamic risk-measures.
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 fully-dynamic risk-indifference pricing is a well set convex price system.
The presentation is based on joint works with Jocelyne Bion-Nadal.
-
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 so-called Gamma-Volterra 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).
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 non-semimartingales 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 so-called Gamma-Volterra 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).
Stochastic calculus and control for systems driven by time-changed Levy noises.
-
Di Nunno, Giulia
(2018).
Kyle-Backs equilibrium model with a random time of information release.
Vis sammendrag
We consider the continuous-time version of Kyle-Back’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).
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 non-semimartingales 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 so-called Gamma-Volterra processes.
The presentation is based on joint works with: Andrea Fiacco, Erik H. Karlsen and Josep Vives.
-
Di Nunno, Giulia
(2018).
Malliavin Calculus and Applications to Finance.
-
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).
On the integration with respect to Volterra processes: fractional calculus and approximation.
-
Di Nunno, Giulia
(2018).
Fully dynamic risk-indifference pricing and no-good-deal 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 fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic 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 time-consistency 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 risk-indifference price with no-good-deal bounds. We recall that no-good-deal 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 risk-indifference prices satisfy the no-good-deal bounds.
In this way no-good-deal bounds provide a way to select the risk measures to obtain a proper fully-dynamic risk-indifference price system.
The presentation is based on various joint works with Jocelyne Bion-Nadal.
-
Di Nunno, Giulia
(2018).
Kyle-Back’s model with a random horizon.
Vis sammendrag
The continuous-time 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).
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
(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 time-consistency to guarantee that the fundamental economic criteria of the non-arbitrage principle is maintained. Various properties and form of pricing operators are presented.
This talk is based on a series of works with various co-authors: Sergio Albeverio (U. Bonn), Jocelyne Bion-Nadal (CNRS Ecole Polytechnique), Inga B. Eide (now at Finanstilsynet), Yuri Rozanov (CNR Milano).
-
Di Nunno, Giulia
(2018).
Kyle-Backs equilibrium model with a random time of information release.
Vis sammendrag
The continuous-time 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
(2017).
Malliavin Calculus for Lévy processes and Time-Change.
-
Di Nunno, Giulia
(2017).
Introduction to Levy Processes and Applications to Finance.
-
Di Nunno, Giulia
(2017).
Fully-dynamic risk-indifference pricing with no-good-deal bounds
.
Vis sammendrag
We deal with the pricing of claims in an incomplete market and we focus on risk-indifference pricing techniques. We propose a fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic 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 risk-indifference 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 L2-framework where we can exploit the dynamic no-good- deal bounds to obtain a complete characterization of these dynamic prices. We shall recall that no-good-deal 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 Bion-Nadal
-
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 fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic 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 fully-dynamic risk-indifference price with no-good-deal bounds. Recall that no-good-deal 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 risk-indifference prices satisfy the no-good-deal bounds.
As it turns out, no-good-deal bounds also provide a method to select the risk measures that provide a proper fully-dynamic risk-indifference price system.
The presentation is based on joint works with Jocelyne Bion-Nadal.
-
Di Nunno, Giulia
(2017).
Fully-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 fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic 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 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 risk-indifference 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 fully-dynamic risk-indifference price with no-good-deal bounds. Recall that no-good-deal 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 risk-indifference prices satisfy the no-good-deal bounds.
As it turns out, no-good-deal bounds also provide a method to select the risk measures that provide a proper fully-dynamic risk-indifference price system.
Based on joint work with Jocelyne Bion-Nadal