Frank Norbert Proske

• Kersting, Hans; Orvieto, Antonio; Proske, Frank Norbert & Lucchi, Aurelien (2022). Mean first exit times of Ornstein-Uhlenbeck processes in high-dimensional spaces. arXiv.org. ISSN 2331-8422.
• Coffie, Emmanuel; Mao, Xuerong & Proske, Frank Norbert (2022). On the Analysis of a Generalised Rough Ait-Sahalia Interest Rate Model. arXiv.org. ISSN 2331-8422.
• Kalinin, Alexander; Meyer-Brandis, Thilo & Proske, Frank Norbert (2022). Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments. arXiv.org. ISSN 2331-8422.
• Harang, Fabian Andsem; Nilssen, Torstein & Proske, Frank Norbert (2022). Girsanov theorem for multifractional Brownian processes. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508.
• Orvieto, Antonio; Kersting, Hans; Proske, Frank Norbert; Bach, Francis & Lucchi, Aurelien (2022). Anticorrelated Noise Injection for Improved Generalization. Proceedings of Machine Learning Research (PMLR). ISSN 2640-3498.
• Lucchi, Aurelien; Proske, Frank Norbert; Orvieto, Antonio; Bach, Francis & Kersting, Hans (2022). On the Theoretical Properties of Noise Correlation in Stochastic Optimization. Advances in Neural Information Processing Systems. ISSN 1049-5258.
• Coffie, Emmanuel; Duedahl, Sindre & Proske, Frank Norbert (2022). Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut-Elworthy-Li formula for singular SDEs. Stochastic Processes and their Applications. ISSN 0304-4149. 156, s. 156–195. doi: 10.1016/j.spa.2022.11.001.
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt Karsten & Proske, Frank Norbert (2022). Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow. Theory of Probability and its Applications. ISSN 0040-585X. 66(4), s. 601–612. doi: 10.1137/S0040585X97T990642.
• Harang, Fabian Andsem; Nilssen, Torstein & Proske, Frank Norbert (2022). GIRSANOV THEOREM FOR MULTIFRACTIONAL BROWNIAN PROCESSES. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2022.2027948. Fulltekst i vitenarkiv
• Baños, David; Ortiz-Latorre, Salvador; Pilipenko, Andrey & Proske, Frank Norbert (2021). Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise. Journal of theoretical probability. ISSN 0894-9840. doi: 10.1007/s10959-021-01084-7. Fulltekst i vitenarkiv
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt Karsten & Proske, Frank Norbert (2021). Optimal stopping, randomized stopping and singular control with general information flow . Theory of Probability and its Applications. ISSN 0040-585X. 66(4), s. 760–773. doi: 10.4213/tvp5514.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2020). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths. arXiv.org. ISSN 2331-8422.
• Amine, Oussama; Baños, David & Proske, Frank Norbert (2020). Regularity properties of the stochastic flow of a skew fractional Brownian motion. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 23(1). doi: 10.1142/S0219025720500058. Fulltekst i vitenarkiv
• Amine, Oussama; Coffie, Emmanuel; Harang, Fabian Andsem & Proske, Frank Norbert (2020). Bismut–Elworthy–Li formula, singular SDEs, fractional Brownian motion, Malliavin calculus, stochastic flows, stochastic volatility. Communications in Mathematical Sciences. ISSN 1539-6746. 18(7), s. 1863–1890. doi: 10.4310/CMS.2020.v18.n7.a3.
• Baños, David; Bauer, Martin; Meyer-Brandis, Thilo & Proske, Frank Norbert (2019). Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise. arXiv.org. ISSN 2331-8422. Fulltekst i vitenarkiv
• Agram, Nacira; Bachouch, Achref; Øksendal, Bernt & Proske, Frank Norbert (2019). Singular control and optimal stopping of memory mean-field processes. SIAM Journal on Mathematical Analysis. ISSN 0036-1410. 51(1), s. 450–468. doi: 10.1137/18M1174787.
• Banos, David; Bølviken, Erik; Duedahl, Sindre & Proske, Frank Norbert (2019). Modeling and estimation of stochastic transition rates in life insurance with regime switching based on generalized Cox processes. Scandinavian Actuarial Journal. ISSN 0346-1238. doi: 10.1080/03461238.2019.1636858. Fulltekst i vitenarkiv Vis sammendrag

  In this paper we aim at modeling stochastic transition rates of state processes in life insurance by using generalized Cox processes. A feature of a our non-Gaussian model is that it can be used to capture ‘regime switching’ effects of data which may be due to regulatory changes in insurance markets or external ‘shocks’ caused e.g. by an economical crisis, natural disasters or epidemics. We propose a method how to estimate the unknown parameters of our model for stochastic transition rates from insurance data by using non-linear filtering techniques for Lévy processes. As a result we also obtain an explicit formula for the unnormalized density of a filtering problem with singular coefficients.

• Baños, David Ruiz; Nilssen, Torstein Kastberg & Proske, Frank Norbert (2019). Strong Existence and Higher Order Fréchet Differentiability of Stochastic Flows of Fractional Brownian Motion Driven SDEs with Singular Drift. Journal of Dynamics and Differential Equations. ISSN 1040-7294. 32, s. 1819–1866. doi: 10.1007/s10884-019-09789-4. Fulltekst i vitenarkiv Vis sammendrag

  In this paper we present a new method for the construction of strong solutions of SDE’s with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter H<1/2. Furthermore, we prove the rather surprising result of the higher order Fréchet differentiability of stochastic flows of such SDE’s in the case of a small Hurst parameter. In establishing these results we use techniques from Malliavin calculus combined with new ideas based on a “local time variational calculus”. We expect that our general approach can be also applied to the study of certain types of stochastic partial differential equations as e.g. stochastic conservation laws driven by rough paths.

• Baños, David; Di Nunno, Giulia; Haferkorn, Hannes Hagen & Proske, Frank Norbert (2018). Stochastic functional differential equations and sensitivity to their initial path. I Celledoni, Elena; Di Nunno, Giulia; Ebrahimi-Fard, Kurusch & Munthe-Kaas, Hans (Red.), Computation and Combinatorics in Dynamics, Stochastics and Control. Springer. ISSN 978-3-030-01592-3. s. 37–70. doi: 10.1007/978-3-030-01593-0_2. Vis sammendrag

  The Abel Symposia volume at hand contains a collection of high-quality 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 16-19 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.

• Agram, Nacira; Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2018). Optimal stopping, randomized stopping and singular control with partial information flow. arXiv.org. ISSN 2331-8422.
• Amine, Oussama; Banos, David & Proske, Frank Norbert (2018). Regularity Properties of the Stochastic Flow of a Skew Fractional Brownian Motion. arXiv.org. ISSN 2331-8422. doi: 10.1142/s0219025720500058.
• Amine, Oussama; Coffie, Emmanuel; Harang, Fabian Andsem & Proske, Frank Norbert (2018). A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling. arXiv.org. ISSN 2331-8422.
• Bauer, Martin; Meyer-Brandis, Thilo & Proske, Frank Norbert (2018). Strong solutions of mean-field stochastic differential equations with irregular drift. Electronic Journal of Probability (EJP). ISSN 1083-6489. 23(132), s. 1–35. doi: 10.1214/18-EJP259. Fulltekst i vitenarkiv
• Pilipenko, Andrey & Proske, Frank Norbert (2018). On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise. Statistics and Probability Letters. ISSN 0167-7152. 132, s. 62–73. doi: 10.1016/j.spl.2017.09.005.
• Pilipenko, Andrey & Proske, Frank Norbert (2018). On a selection problem for small noise perturbation in the multidimensional case. Stochastics and Dynamics. ISSN 0219-4937. 18(6). doi: 10.1142/S0219493718500454. Fulltekst i vitenarkiv
• Baños, David Ruiz; Duedahl, Sindre; Meyer-Brandis, Thilo & Proske, Frank Norbert (2018). Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle. Annales de l'I.H.P. Probabilites et statistiques. ISSN 0246-0203. 54(3), s. 1464–1491. doi: 10.1214/17-AIHP845. Fulltekst i vitenarkiv
• Baños, David Ruiz & Proske, Frank Norbert (2017). C-infinity-regularization by Noise of Singular ODE's. arXiv.org. ISSN 2331-8422. Fulltekst i vitenarkiv
• Baños, David Ruiz; Haferkorn, Hannes Hagen & Proske, Frank Norbert (2017). Strong Uniqueness of Singular Stochastic Delay Equations. arXiv.org. ISSN 2331-8422.
• Baños, David Ruiz; Meyer-Brandis, Thilo; Proske, Frank Norbert & Duedahl, Sindre (2017). Computing Deltas without Derivatives. Finance and Stochastics. ISSN 0949-2984. 21(2), s. 509–549. doi: 10.1007/s00780-016-0321-3. Fulltekst i vitenarkiv
• Pilipenko, Andrey & Proske, Frank Norbert (2016). On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise. arXiv.org. ISSN 2331-8422. doi: 10.1016/j.spl.2017.09.005.
• Pilipenko, Andrey & Proske, Frank Norbert (2015). On a Selection Problem for Small Noise Perturbation in Multidimensional Case. arXiv.org. ISSN 2331-8422. doi: 10.1142/s0219493718500454.
• Banos, David Ruiz; Nilssen, Torstein Kastberg & Proske, Frank Norbert (2015). Strong existence and higher order Fréchet differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift. arXiv.org. ISSN 2331-8422. doi: 10.1007/s10884-019-09789-4.
• Mohammed, Salah-Eldin; Nilssen, Torstein Kastberg & Proske, Frank Norbert (2015). Sobolev differentiable stochastic flows for sdes with singular coefficients: Applications to the transport equation. Annals of Probability. ISSN 0091-1798. 43(3), s. 1535–1576. doi: 10.1214/14-AOP909.
• Haadem, Sven & Proske, Frank Norbert (2014). On the Construction and Malliavin Differentiability of Solutions of Levy Noise driven SDE's with Singular Coefficients. Journal of Functional Analysis. ISSN 0022-1236. 266(8), s. 5321–5359. doi: 10.1016/j.jfa.2014.02.009.
• Bølviken, Erik; Proske, Frank Norbert & Rubtsov, Mark (2014). Pricing of Margrabe options for large investors with application to asset-liability management in life insurance. Journal of Mathematical Finance. ISSN 2162-2434. 4(2), s. 113–122. doi: 10.4236/jmf.2014.42011.
• Pamen, Olivier Menoukeu; Proske, Frank Norbert & Salleh, Hassilah Binti (2014). Stochastic differential games in insider markets via Malliavin calculus. Journal of Optimization Theory and Applications. ISSN 0022-3239. 160(1), s. 302–343. doi: 10.1007/s10957-013-0310-z.
• Kettler, Paul Carlisle; Yablonski, Aleh & Proske, Frank Norbert (2013). Market microstructure and price discovery. Journal of Mathematical Finance. ISSN 2162-2434. 3(1). doi: 10.4236/jmf.2013.31001.
• Menoukeu Pamen, Olivier; Meyer-Brandis, Thilo; Proske, Frank Norbert & Salleh, Hassilah Binti (2013). Malliavin Calculus Applied to Optimal Control of Stochastic Partial Differential Equations with Jumps. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 85(3), s. 431–463. doi: 10.1080/17442508.2011.652964.
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2013). A maximum principle for infinite horizon delay equations. SIAM Journal on Mathematical Analysis. ISSN 0036-1410. 45, s. 2499–2522. doi: 10.1137/120882809.
• Flandoli, Franco; Nilssen, Torstein Kastberg & Proske, Frank Norbert (2013). Malliavin differentiability and strong solutions for a class of SDE in Hilbert spaces. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. Fulltekst i vitenarkiv
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2013). A maximum principle for infinite horizon delay equatations. SIAM Journal on Mathematical Analysis. ISSN 0036-1410. 45(4), s. 2499–2522. doi: 10.1137/120882809. Fulltekst i vitenarkiv
• Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2013). Maximum principles for jump diffusion processes with infinite horizon. Automatica. ISSN 0005-1098. 49(7), s. 2267–2275. doi: 10.1016/j.automatica.2013.04.011. Fulltekst i vitenarkiv
• Menoukeu, Olivier Pamen; Meyer-Brandis, Thilo; Nilssen, Torstein Kastberg; Proske, Frank Norbert & Zhang, Tusheng (2013). A variational approach to the construction and Malliavin differentiability of strong solutions of SDE's. Mathematische Annalen. ISSN 0025-5831. 357(2), s. 761–799. doi: 10.1007/s00208-013-0916-3.
• Yolcu, Okur Yeliz; Proske, Frank Norbert & Salleh, Hassilah Binti (2012). SDE Solutions in the Space of Smooth Random Variables. Communications on Stochastic Analysis. ISSN 0973-9599. 6(3), s. 451–470. doi: 10.31390/cosa.6.3.07.
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2012). A MAXIMUM PRINCIPLE FOR INFINITE HORIZON DELAY EQUATIONS. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. 4. Fulltekst i vitenarkiv
• Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2012). Maximum principles for jump diffusion processes with infinite horizon. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. April(3). doi: 10.1016/j.automatica.2013.04.011. Fulltekst i vitenarkiv
• Proske, Frank Norbert; Rubtsov, Mark & Ta, An Thi Kieu (2011). RISK INDIFFERENCE PRICING OF FUNCTIONAL CLAIMS OF THE YIELD SURFACE IN THE PRESENCE OF PARTIAL INFORMATION TA. Communications on Stochastic Analysis. ISSN 0973-9599. 5(3), s. 541–563. doi: 10.31390/cosa.5.3.06.
• Mandrekar, Vidyadhar; Meyer-Brandis, Thilo & Proske, Frank Norbert (2011). A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise. Journal of Probability and Statistics. ISSN 1687-952X. doi: 10.1155/2011/259091.
• Di Nunno, Giulia; Pamen, Olivier Menoukeu; Øksendal, Bernt & Proske, Frank Norbert (2011). A general maximum principle for anticipative stochastic control and applications to insider trading. I Di Nunno, Giulia & Øksendal, Bernt (Red.), Advanced Mathematical Methods for Finance. Springer. ISSN 978-3-642-18411-6. s. 181–221. doi: 10.1007/978-3-642-18412-3_7.
• Di Nunno, Giulia; Øksendal, Bernt; Menoukeu Pamen, Olivier & Proske, Frank Norbert (2011). Uniqueness of Decompositions of Skorohod-Semimartingales. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 14(1), s. 15–24. doi: 10.1142/S0219025711004274.
• Kettler, Paul Carlisle; Proske, Frank Norbert & Rubtsov, Mark (2011). Sensitivity with respect to the yield curve: duration in a stochastic setting. Springer Series in Statistics. ISSN 0172-7397. s. 363–385. doi: 10.1007/978-3-319-02069-3_17.
• Meyer-Brandis, Thilo & Proske, Frank Norbert (2010). Construction of strong solutions of SDE's via Malliavin calculus. Journal of Functional Analysis. ISSN 0022-1236. 258(11), s. 3922–3953. doi: 10.1016/j.jfa.2009.11.010.
• Menoukeu, Olivier Pamen; Meyer-Brandis, Thilo & Proske, Frank Norbert (2010). A Gel'fand triple approach to the small noise problem for discontinuous ODE's. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• An, Ta Thi Kieu; Proske, Frank Norbert & Rubtsov, Mark (2010). Risk Indifference Pricing of Functional Claims of the Yield Surface in the Presence of Partial Information. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Ta, An Thi Kieu; Proske, Frank Norbert & Rubtsov, Mark (2010). A SPDE maximum principle for stochastic differential games under partial information with application to optimal portfolios on fixed income markets. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 82(1), s. 3–23. doi: 10.1080/17442500902723542.
• Meyer-Brandis, Thilo & Proske, Frank Norbert (2010). Explicit Representation of Strong Solutions of SDEs Driven by Infinite-Dimensional L,vy Processes. Journal of theoretical probability. ISSN 0894-9840. 23(1), s. 301–314. doi: 10.1007/s10959-009-0226-6.
• Benth, Fred Espen & Proske, Frank Norbert (2009). Utility indifference pricing of interest rate guarantees. International Journal of Theoretical and Applied Finance. ISSN 0219-0249. 12(1), s. 63–82. doi: 10.1142/S0219024909005117.
• Meyer-Brandis, Thilo & Proske, Frank Norbert (2009). Explicit Representation of Strong Solutions of SDEs Driven by Infinite-Dimensional Lévy Processes. Journal of theoretical probability. ISSN 0894-9840. s. 1–14. doi: 10.1007/s10959-009-0226-6.
• Ocur, Yeliz Yolcu; Proske, Frank Norbert & Salleh, Hassilah Binti (2009). SDE solutions in the space of smooth random variables. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. 11.
• Di Nunno, Giulia; Øksendal, Bernt; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2009). A general maximum principle for anticipative stochastic control and applications to insider trading. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Pamen, Olivier Menoukeu; Proske, Frank Norbert & Salleh, Hassilah Binti (2009). Stochastic Differential Games in Insider Markets via Malliavin Calculus. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Henriksen, Pål Nikolai; Hove, Arne; Meyer-Brandis, Thilo & Proske, Frank Norbert (2009). Pricing interest rate guarantees in a defined benefit pension system. Statistical research report (Universitetet i Oslo. Matematisk institut. ISSN 0806-3842.
• Di Nunno, Giulia; Øksendal, Bernt; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2009). Uniqueness of Decompositions of Skorohod-Semimartingales. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Kettler, Paul Carlisle; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2009). On Local Times: Application to Pricing Using Bid-Ask. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Di Nunno, Giulia; Øksendal, Bernt; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2009). Uniqueness of Decompositions of Skorohod-Semimartingales. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Di Nunno, Giulia; Kohatsu-Higa, Arturo; Meyer-Brandis, Thilo; Øksendal, Bernt; Proske, Frank Norbert & Sulem, Agnès (2008). Anticipative stochastic control for Lévy processes with application to insider trading. I Bensoussan, Alain; Qiang, Zhang & Ciarlet, Philippe G (Red.), MATHEMATICAL MODELLING AND NUMERICAL METHODS IN FINANCE. Elsevier. ISSN 978-0-444-51879-8.
• Øksendal, Bernt; Proske, Frank Norbert & Ta, An Thi Kieu (2008). A Maximum Principle Approach to Risk Indifference Pricing with Partial Information. Journal of Applied Mathematics and Stochastic Analysis. ISSN 1048-9533. 2008(3). doi: 10.1155/2008/821243.
• An, Ta Thi Kieu; Proske, Frank Norbert & Rubtsov, Mark (2008). A SPDE Maximum Principle for Stochastic Differential Games under Partial Information with Application to Optimal Portfolios on Fixed Income Markets. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508.
• Meyer-Brandis, Thilo & Proske, Frank Norbert (2008). Explicit representation of strong solutions of SDE's driven by infinite dimensional Lévy processes. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. s. 1–18.
• Ta, An Thi Kieu; Proske, Frank Norbert & Rubtsov, Mark (2007). A SPDE maximum principle for stochastic differential games under partial information with application to optimal portfolios on fixed income markets. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Menoukeu, Olivier Pamen; Meyer-Brandis, Thilo; Proske, Frank Norbert & Salleh, Hassilah B. (2007). Malliavin calculus applied to optimal control of stochastic partial differential equations with jumps. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.
• Proske, Frank Norbert (2007). Stochastic differential equations- some new ideas. Stochastics and Stochastics Reports. ISSN 1045-1129. 79(6), s. 563–600.
• Løkka, Arne & Proske, Frank Norbert (2006). Infinite dimensional analysis of pure jump Levy processes on Poisson space. Mathematica Scandinavica. ISSN 0025-5521. 98, s. 237–261.
• Meyer-Brandis, Thilo & Proske, Norbert Frank (2006). On the existence and explicit representability of strong solutions of Levy noise driven SDE's with irregular coefficients. Communications in Mathematical Sciences. ISSN 1539-6746. 4(1).
• Di Nunno, Giulia; Meyer-Brandis, Thilo; Øksendal, Bernt & Proske, Norbert Frank (2006). Optimal portfolio for an insider in a market driven by Levy processes. Quantitative finance (Print). ISSN 1469-7688. 6, s. 83–94.
• Øksendal, Bernt; Proske, Norbert Frank & Signahl, Mikael (2006). The Cauchy problem for the wave equation with Levy noise initial data. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 9, s. 249–270.
• Di Nunno, Giulia; Meyer-Brandis, Thilo; Øksendal, Bernt & Proske, Frank Norbert (2005). Malliavin calculus and anticipative Ito formulae for Levy processes. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 8(2), s. 235–258. doi: 10.1142/S0219025705001950. Vis sammendrag

  We introduce the forward integral with respect to a pure jump Lévy process and we prove and formula for this integral. Then we use Mallivin calculus to establish a relationship between the forward integral and the Skorohod integral and we apply this to obtain an Itô formula for the Skorohod integral.

• Di Nunno, Giulia; Meyer-Brandis, Thilo; Øksendal, Bernt & Proske, Norbert Frank (2005). Malliavin calculus and anticipative Ito formulae for Levy processes. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 8, s. 235–258.
• Di Nunno, Giulia; Kohatsu-Higa, Arturo; Meyer-Brandis, Thilo; Proske, Frank Norbert; Øksendal, Bernt & Sulem, Agnès (2005). Optimal portfolio for a "large" insider in a market driven by Lévy processes. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439.

Se alle arbeider i Cristin

• Di Nunno, Giulia; Øksendal, Bernt & Proske, Frank Norbert (2009). Malliavin Calculus for Lévy Processes and Applications to Finance. Springer. ISBN 978-3-540-78571-2. 413 s.

Se alle arbeider i Cristin

• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2022). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2022). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2020). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Proske, Frank Norbert (2019). Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial nise.
• Baños, David Ruiz; Ortiz-Latorre, Salvador; Pilipenko, Andrey & Proske, Frank Norbert (2017). Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise.
• Nilssen, Torstein Kastberg; Baños, David Ruiz & Proske, Frank Norbert (2016). Strong Existence and higher order differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift.
• Proske, Frank Norbert & Haadem, Sven (2014). On the construction and Malliavin differentiability of solutions of Lévy noise driven SDE's with singular coefficients.
• Haadem, Sven & Proske, Frank Norbert (2013). On the Construction and Malliavin Differentiability of Strong Solutions to Levy Noise Driven SDEs with Singular Coefficients.
• Proske, Frank Norbert (2012). Construction and Malliavin differentiability of strong solutions of SDEs with merely measurable drift.
• Di Nunno, Giulia; L'Aurora, Edoardo; Moschetta, Marina; Proske, Frank Norbert & Ruiz-Banos, David (2012). Market with memory and sensitivity to the past.
• Di Nunno, Giulia; L'Aurora, Edoardo; Moschetta, Marina; Proske, Frank Norbert & Ruiz-Banos, David (2012). Market with memory: pricing and sensitivity analysis.
• Proske, Frank Norbert (2010). Computing Greeks without Derivatives (joint paper with Menoukeu-Pamen, O., Meyer-Brandis, T. in progress).
• Henriksen, Pål Nikolai; Hove, Arne; Meyer-Brandis, Thilo & Proske, Frank Norbert (2009). Pricing interest rate guarantees in Norwegian defined benefit pension.
• Proske, Frank Norbert (2009). Construction of Strong Solutions of SDE's via Malliavin Calculus.
• Proske, Frank Norbert (2008). On the construction of strong solutions of SDE's without pathwise uniqueness.
• Proske, Frank Norbert (2008). "Gratis lunsj" og finans.
• Nilssen, Torstein Kastberg; Mohammed, Salah-Eldin & Proske, Frank Norbert (2012). Sobolev Differentiable Stochastic Flows for SDE’s with SingularCoefficients: Applications to the Transport Equation. Matematisk institutt, UiO. Fulltekst i vitenarkiv
• Meyer-Brandis, Thilo; Nilssen, Torstein Kastberg; Pamen, Olivier Menoukeu; Proske, Frank Norbert & Zhang, Tusheng (2011). A variational approach to the construction and Malliavin differentiability of strong solutions of SDE's. Universitetet i Oslo. ISSN 0806-2439. Fulltekst i vitenarkiv
• Meyer-Brandis, Thilo; Proske, Frank Norbert & Mandrekar, Vidyadhar (2007). A Bayes formula for non-linear filtering with Gaussian and Cox noise. Preprint Series in Pure Mathematics (13).
• Di Nunno, Giulia; Kohatsu-Higa, Arturo; Meyer-Brandis, Thilo; Øksendal, Bernt; Proske, Frank Norbert & Sulem, Agnès (2005). Optimal Portfolio for a "large" Insider in a Market driven by Lévy Processes. Universitetet i Oslo. Vis sammendrag

  An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market. In this paper we consider the optimization problem of an insider who is so influential in the market to affect the price dynamics: in this sense he is called a "large" insider. The optimal portfolio problem for a general utility function is studied for a financial market driven by a Lévy process in the framework of forward anticipating calculus.

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