Bernt Karsten Øksendal

• Agram, Nacira; Pucci, Giulia & Øksendal, Bernt Karsten (2024). Impulse Control of Conditional McKean–Vlasov Jump Diffusions. Journal of Optimization Theory and Applications. ISSN 0022-3239. doi: 10.1007/s10957-023-02370-6.
• Øksendal, Bernt Karsten (2023). Space-time stochastic calculus and white noise. In Morel, Jean-Michel & Teissier, Bernard (Ed.), Mathematics Going Forward - Collected Mathematical Brushstrokes. Springer. ISSN 978-3-031-12243-9. p. 629–649. Full text in Research Archive
• Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2023). Optimal control of SPDEs driven by time-space Brownian motion . arXiv.org. ISSN 2331-8422.
• Agram, Nacira & Øksendal, Bernt Karsten (2023). The Donsker delta function and local time for McKean–Vlasov processes and applications. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2023.2286252. Full text in Research Archive
• Makhlouf, K.; Agram, Nacira; Hilbert, A. & Øksendal, Bernt Karsten (2023). SPDEs with space interactions and application to population modelling. ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV). ISSN 1292-8119. 29. doi: 10.1051/cocv/2023010. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt Karsten (2023). Stochastic Fokker–Planck Equations for Conditional McKean–Vlasov Jump Diffusions and Applications to Optimal Control. SIAM Journal of Control and Optimization. ISSN 0363-0129. 61(3), p. 1472–1493. doi: 10.1137/21M1461034. Full text in Research Archive
• Moulay Hachemi, Rahma Yasmina & Øksendal, Bernt Karsten (2023). The fractional stochastic heat equation driven by time-space white noise. Fractional Calculus and Applied Analysis. ISSN 1311-0454. 26(2), p. 513–532. doi: 10.1007/s13540-023-00134-7. Full text in Research Archive
• Agram, Nacira; Labed, Saloua; Øksendal, Bernt Karsten & Yakhlef, Samia (2022). Singular Control of Stochastic Volterra Integral Equations. Acta Mathematica Scientia. ISSN 0252-9602. 42(3), p. 1003–1017. doi: 10.1007/s10473-022-0311-9. Full text in Research Archive
• Agram, Nacira; Hu, Yaozhong & Øksendal, Bernt Karsten (2022). Mean-field backward stochastic differential equations and applications. Systems & control letters (Print). ISSN 0167-6911. 162. doi: 10.1016/j.sysconle.2022.105196. Full text in Research Archive
• 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), p. 760–773. doi: 10.4213/tvp5514.
• Agram, Nacira & Øksendal, Bernt (2020). A financial market with singular drift and no arbitrage. Mathematics and Financial Economics. ISSN 1862-9679. doi: 10.1007/s11579-020-00284-9. Full text in Research Archive
• Draouil, Olfa & Øksendal, Bernt (2019). A white noise approach to optimal insider control of systems with delay. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 476(1), p. 101–119. doi: 10.1016/j.jmaa.2019.02.065. Full text in Research Archive
• Agram, Nacira; Hilbert, Astrid & Øksendal, Bernt (2019). Singular control of SPDEs with space-mean dynamics. Mathematical Control and Related Fields. ISSN 2156-8472. doi: 10.3934/mcrf.2020004. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt (2019). Mean-field stochastic control with elephant memory in infinite time horizon. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 91(7), p. 1041–1066. doi: 10.1080/17442508.2019.1635600. Full text in Research Archive
• Draouil, Olfa & Øksendal, Bernt (2019). Viable insider markets. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 91(7), p. 959–973. doi: 10.1080/17442508.2019.1612895. Full text in Research Archive
• Agram, Nacira; Øksendal, Bernt & Yakhlef, Samia (2019). New approach to optimal control of stochastic Volterra integral equations. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 91(6), p. 873–894. doi: 10.1080/17442508.2018.1557186. Full text in Research Archive
• 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), p. 450–468. doi: 10.1137/18M1174787.
• Agram, Nacira & Øksendal, Bernt (2019). Model uncertainty stochastic mean-field control. Stochastic Analysis and Applications. ISSN 0736-2994. 37(1), p. 36–56. doi: 10.1080/07362994.2018.1499036. Full text in Research Archive
• Dumitrescu, Roxana; Øksendal, Bernt & Sulem, Agnès (2018). Stochastic control of general mean-field SPDEs with jumps. Journal of Optimization Theory and Applications. ISSN 0022-3239. 176(3), p. 559–584. doi: 10.1007/s10957-018-1243-3. Full text in Research Archive
• Biagini, Francesca; Meyer-Brandis, Thilo; Øksendal, Bernt & Paczka, Krzysztof Jaroslaw (2018). Optimal control with delayed information flow of systems driven by G-Brownian motion. Probability, Uncertainty and Quantitative Risk (PUQR). ISSN 2095-9672. 3. doi: 10.1186/s41546-018-0033-z.
• 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.
• Agram, Nacira; Hilbert, Astrid & Øksendal, Bernt (2018). SPDEs with Space-Mean Dynamics. arXiv.org. ISSN 2331-8422. doi: 10.3934/mcrf.2020004.
• Agram, Nacira & Øksendal, Bernt (2018). Mean-Field Stochastic Control with Elephant Memory in Finite and Infinite Time Horizon. arXiv.org. ISSN 2331-8422. doi: 10.1080/17442508.2019.1635600.
• Agram, Nacira; Øksendal, Bernt & Yakhlef, Samia (2018). Optimal control of forward-backward stochastic Volterra equations, Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume. European Mathematical Society (EMS) Press. ISSN 978-3-03719-186-6. p. 3–36.
• Agram, Nacira & Øksendal, Bernt (2018). A Hida-Malliavin white noise calculus approach to optimal control. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 21(3), p. 1850014-1–1850014-21. doi: 10.1142/S0219025718500145. Full text in Research Archive
• Hu, Yaozhong & Øksendal, Bernt (2018). Linear Volterra backward stochastic integral equations. Stochastic Processes and their Applications. ISSN 0304-4149. 129(2), p. 626–633. doi: 10.1016/j.spa.2018.03.016. Full text in Research Archive
• Dumitrescu, Roxana; Øksendal, Bernt & Sulem, Agnès (2018). Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps. Journal of Optimization Theory and Applications. ISSN 0022-3239. 176(3), p. 559–584. doi: 10.1007/s10957-018-1243-3.
• Agram, Nacira; Hu, Yaozhong & Øksendal, Bernt (2018). Mean-field backward stochastic differential equations and applications. arXiv.org. ISSN 2331-8422.
• Draouil, Olfa & Øksendal, Bernt (2018). Optimal insider control of stochastic partial differential equations. Stochastics and Dynamics. ISSN 0219-4937. 18(1). doi: 10.1142/S0219493718500144. Full text in Research Archive
• Agram, Nacira; Øksendal, Bernt & Yakhlef, Samia (2017). New approach to optimal control of stochastic Volterra integral equations. arXiv.org. ISSN 2331-8422. p. 1–22. doi: 10.1080/17442508.2018.1557186.
• Agram, Nacira & Øksendal, Bernt (2017). Stochastic control of memory mean-field processes. Applied Mathematics and Optimization. ISSN 0095-4616. p. 1–24. doi: 10.1007/s00245-017-9425-1. Full text in Research Archive
• Øksendal, Bernt & Røse, Elin Engen (2017). A white noise approach to insider trading. In Hida, Takeyuki & Streit, Ludwig (Ed.), Let Us Use White Noise. World Scientific. ISSN 978-981-3220-93-5. p. 191–204. doi: 10.1142/9789813220942_0006. Full text in Research Archive Show summary

  We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.

• Dahl, Kristina Rognlien & Øksendal, Bernt (2017). Singular recursive utility. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 89(6-7), p. 994–1014. doi: 10.1080/17442508.2017.1303067. Full text in Research Archive
• Hu, Yaozhong; Øksendal, Bernt & Sulem, Agnes Biacobroda (2017). Singular mean-field control games. Stochastic Analysis and Applications. ISSN 0736-2994. 35(5), p. 823–851. doi: 10.1080/07362994.2017.1325745. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2016). Optimal control of predictive mean-field equations and applications in finance. In Benth, Fred Espen & Di Nunno, Giulia (Ed.), Stochastics of Environmental and Financial Economics. Springer Science+Business Media B.V.. ISSN 978-3-319-23424-3. doi: 10.1007/978-3-319-23425-0_12.
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2016). A stochastic HJBI equation for optimal control of forward-backward SDEs. In Podolskij, Mark; Stelzer, Robert; Thorbjørnsen, Steen & Veraart, Almut E. D. (Ed.), The Fascination of Probability, Statistics and their Applications. In honour of Ole E. Barndorff-Nielsen. Springer Science+Business Media B.V.. ISSN 978-3-319-25824-9.
• Agram, Nacira; Øksendal, Bernt & Yakhlef, Samia (2016). Optimal control of forward-backward stochastic Volterra equations. arXiv.org. ISSN 2331-8422. doi: 10.4171/186-1/1.
• Agram, Nacira & Øksendal, Bernt (2016). Model Uncertainty Stochastic Mean-Field Control. arXiv.org. ISSN 2331-8422. doi: 10.1080/07362994.2018.1499036.
• Øksendal, Bernt; Sulem, Agnes Biacobroda & Zhang, Tusheng (2016). A stochastic HJB equation for optimal control of forward-backward SDEs. In Podolskij, Mark; Stelzer, Robert; Thorbjørnsen, Steen & Veraart, Almut E. D. (Ed.), The Fascination of Probability, Statistics and their Applications. In honour of Ole E. Barndorff-Nielsen. Springer Science+Business Media B.V.. ISSN 978-3-319-25824-9. p. 435–446. doi: 10.1007/978-3-319-25826-3_20. Show summary

  We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the Itô-Ventzell formula, the system is transformed into a controlled backward stochastic partial differential equation. Using a comparison principle for such equations we obtain a general stochastic Hamilton-Jacobi-Bellman (HJB) equation for the value function of the control problem. In the case of Markovian optimal control of jump diffusions, this equation reduces to the classical HJB equation. The results are applied to study risk minimization in financial markets.

• Draouil, Olfa & Øksendal, Bernt (2016). Optimal insider control and semimartingale decompositions under enlargement of filtration. Stochastic Analysis and Applications. ISSN 0736-2994. 34(6), p. 1045–1056. doi: 10.1080/07362994.2016.1200989. Full text in Research Archive
• Draouil, Olfa & Øksendal, Bernt (2016). Stochastic differential games with inside information. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 19(3). doi: 10.1142/S0219025716500168. Full text in Research Archive
• Dahl, Kristina Rognlien; Mohammed, Salah-Eldin; Øksendal, Bernt & Røse, Elin Engen (2016). Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives. Journal of Functional Analysis. ISSN 0022-1236. 271(2), p. 289–329. doi: 10.1016/j.jfa.2016.04.031. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2016). Dynamic robust duality in utility maximization. Applied Mathematics and Optimization. ISSN 0095-4616. p. 1–31. doi: 10.1007/s00245-016-9329-5. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2016). Optimal control of predictive mean-field equations and applications to finance. Springer Proceedings in Mathematics & Statistics. ISSN 2194-1017. 138, p. 301–320. doi: 10.1007/978-3-319-23425-0_12. Full text in Research Archive Show summary

  We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a predictive mean-field backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of the BSDE at time t may depend not just upon the unknown processes Y(t),Z(t),K(t,⋅), but also on the predicted future value Y(t+δ), defined by the conditional expectation A(t):=E[Y(t+δ)|Ft]. We give a sufficient and a necessary maximum principle for the optimal control of such systems, and then we apply these results to the following two problems: (i) Optimal portfolio in a financial market with an insider influenced asset price process. (ii) Optimal consumption rate from a cash flow modeled as a geometric Itô-Lévy SDE, with respect to predictive recursive utility.

• Alvarez, Luis H.; Lungu, Edward & Øksendal, Bernt (2016). Optimal multi-dimensional stochastic harvesting with density-dependent prices. Afrika Matematika. ISSN 1012-9405. 27(3), p. 427–442. doi: 10.1007/s13370-015-0357-0. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2015). Applications of stochastic analysis. In Higham, Nicholas J. (Eds.), The Princeton Companion to Applied Mathematics. Princeton University Press. ISSN 978-0-691-15039-0.
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2015). A comparison theorem for backward SPDEs with jumps. In Chen, Zhen-Qing (Eds.), Festscrift Masatoshi Fukushima. World Scientific. ISSN 978-9814596527. doi: 10.1142/9789814596534_0023.
• Draouil, Olfa & Øksendal, Bernt (2015). A Donsker delta functional approach to optimal insider control and applications to finance. Communications in Mathematics and Statistics. ISSN 2194-6701. 3(3), p. 365–421. doi: 10.1007/s40304-015-0065-y. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt (2015). Malliavin Calculus and Optimal Control of Stochastic Volterra Equations. Journal of Optimization Theory and Applications. ISSN 0022-3239. 167(3), p. 1070–1094. doi: 10.1007/s10957-015-0753-5. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnes Biacobroda (2015). Risk minimization in financial markets modeled by Itô-Lévy processes. Afrika Matematika. ISSN 1012-9405. 26(5-6), p. 939–979. doi: 10.1007/s13370-014-0248-9. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2014). Forward-Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty. Journal of Optimization Theory and Applications. ISSN 0022-3239. 161(1), p. 22–55. doi: 10.1007/s10957-012-0166-7. Full text in Research Archive
• 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 0806-2439. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnes Biacobroda (2014). Stochastic control of Itô-Lévy processes with applications to finance. Communications on Stochastic Analysis. ISSN 0973-9599. 8(1), p. 1–15. Full text in Research Archive
• Øksendal, Bernt; Sandal, Leif Kristoffer & Ubøe, Jan (2014). Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information. Journal of Applied Probability. ISSN 0021-9002. 51A, p. 213–226. doi: 10.1239/jap/1417528477. Full text in Research Archive
• Fontana, Claudio; Øksendal, Bernt & Sulem, Agnes Biacobroda (2014). Market Viability and Martingale Measures under Partial Information. Methodology and Computing in Applied Probability. ISSN 1387-5841. doi: 10.1007/s11009-014-9397-4. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt (2014). Infinite horizon optimal control of forward-backward stochastic differential equations with delay. Journal of Computational and Applied Mathematics. ISSN 0377-0427. 259, p. 336–349. doi: 10.1016/j.cam.2013.04.048. Full text in Research Archive
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2014). Singular control and optimal stopping of SPDEs, and backward SPDEs with reflection. Mathematics of Operations Research. ISSN 0364-765X. 39(2), p. 464–486. doi: 10.1287/moor.2013.0602. Full text in Research Archive
• Siegmund-Schultze, Reinhard & Øksendal, Bernt (2013). Johannes Lohne (1908-1993), den glemte norske nyoppdager av Thomas Harriot og frontkjemper for den tyske okkupasjonsmakten under 2. verdenskrig. Normat. ISSN 0801-3500. 61(1), p. 18–32.
• 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, p. 2499–2522. doi: 10.1137/120882809.
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2013). A stochastic HJB equation for optimal control of forward-backward SDEs. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. doi: 10.1007/978-3-319-25826-3_20. Full text in Research Archive
• 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), p. 2499–2522. doi: 10.1137/120882809. Full text in Research Archive
• Øksendal, Bernt; Sandal, Leif Kristoffer & Ubøe, Jan (2013). Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models. Journal of Economic Dynamics and Control. ISSN 0165-1889. 37(7), p. 1284–1299. doi: 10.1016/j.jedc.2013.02.010. Full text in Research Archive Show summary

  In this paper, we prove a maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem, a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Itô–Lévy process, and to increase realism information is delayed, e.g., due to production time. A special feature of our time-continuous model is that it allows for a price-dependent demand, thereby opening for strategies where pricing is used to manipulate the demand.

• Baghery, Fouzia; Haadem, Sven; Øksendal, Bernt & Turpin, Isabella (2013). Optimal stopping and stochastic control differential games for jump diffusions. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. 85(1), p. 85–97. doi: 10.1080/17442508.2011.652116. Full text in Research Archive
• Øksendal, Bernt & Sulem, Agnès (2013). A stochastic control approach to robust duality in utility maximization. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. doi: 10.1007/s00245-016-9329-5. Full text in Research Archive
• Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2013). Maximum principles for jump diffusion processes with infinite horizon. Automatica. ISSN 0005-1098. 49(7), p. 2267–2275. doi: 10.1016/j.automatica.2013.04.011. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt (2013). Infinite horizon optimal control of forward-backward stochastic differential equations with delay. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN 0806-2439. doi: 10.1016/j.cam.2013.04.048. Full text in Research Archive
• Øksendal, Bernt & Zhang, Tusheng (2012). Backward stochastic differential equations with respect to general filtrations and applications to insider finance. Communications on Stochastic Analysis. ISSN 0973-9599. 6(4), p. 703–722. doi: 10.31390/cosa.6.4.13. Full text in Research Archive
• Aase, Knut; Bjuland, Terje & Øksendal, Bernt (2012). Strategic insider trading equilibrium: A filter theory approach. Afrika Matematika. ISSN 1012-9405. 23(2), p. 145–162. doi: 10.1007/s13370-011-0026-x. Full text in Research Archive Show summary

  The continuous-time version of Kyle’s (Econometrica 53(6):1315–1336, 1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing time-varying liquidity trading, and by having weaker a priori assumptions on the model. This extension is made possible by the use of filtering theory. We derive the optimal trade for an insider and the corresponding price of the risky asset; the insider’s trading intensity satisfies a deterministic integral equation, given perfect inside information.

• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2012). Optimal partial information control of SPDEs with delay and time-advanced backward SPDEs. In Zhang, Tusheng & Zhou, Xunyu (Ed.), Stochastic Analysis and Applications to Finance. World Scientific. ISSN 978-981-4383-57-8.
• Aase, Knut; Bjuland, Terje & Øksendal, Bernt (2012). Partially informed noise traders. Mathematics and Financial Economics. ISSN 1862-9679. 6(2), p. 93–104. doi: 10.1007/s11579-012-0075-4. Full text in Research Archive Show summary

  The single auction equilibrium of Kyle’s (1985) is studied, in which noise traders may be partially informed, or alternatively they can be manipulated. Unlike Kyle’s assumption that the quantity traded by the noise traders is independent of the asset value, we assume that the noise traders are able to correlate their trade with the true price. This has several implications for the equilibrium, one being that the informed trader’s expected profits decrease as the noise traders’ ability to correlate positively improve. In the limit, the noise traders do not lose on average, and the informed trader makes zero expected profits. When the correlation is negative, we interpret this as manipulation. In this case the insider makes the highest expected profits, and the informativeness of prices is at its minimum.

• Meyer-Brandis, Thilo; Hu, Yaozhong; Øksendal, Bernt & Biagini, Francesca (2012). Insider trading equilibrium in a market with memory. Mathematics and Financial Economics. ISSN 1862-9679. 6, p. 229–247. doi: 10.1007/s11579-012-0065-6.

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• Øksendal, Bernt (2020). A financial market with singular drift and no arbitrage.
• Øksendal, Bernt (2019). Introduction to White Noise Theory and Applications.
• Øksendal, Bernt (2019). Introduction to Stochastic Control Theory for Jump Diffusions.
• Øksendal, Bernt (2019). Introduction to Stochastic Control of Jump Diffusions, with Applications to Mathematical Finance.
• Øksendal, Bernt (2019). A financial market with a local time drift term and delay.
• Øksendal, Bernt (2019). Introduction to White Noise Theory and Applications.
• Øksendal, Bernt (2019). Introduction to Stochastic Control Theory for Jump Diffusions.
• Øksendal, Bernt (2019). A financial market with a local time drift term and delay.
• Øksendal, Bernt (2019). Introduction to Stochastic Control of Jump Diffusions, with Applications to Mathematical Finance.
• Øksendal, Bernt (2018). SPDEs with space - mean dynamics.
• Øksendal, Bernt (2018). Introduction to Stochastic Control and applications.
• Øksendal, Bernt (2018). Optimal control of stochastic Volterra equations.
• Øksendal, Bernt (2018). Optimal control of mean-field stochastic differential equations.
• Øksendal, Bernt (2018). Introduction to Stochastic Control with Applications.
• Øksendal, Bernt (2018). An Introduction to Stochastic Control, with Applications to Mathematical Finance.
• Øksendal, Bernt (2018). New approach to optimal control of stochastic Volterra equations.
• Øksendal, Bernt (2018). Model uncertainty stochastic mean-field control.
• Øksendal, Bernt (2018). Introduction to optimal stochastic control with inside information.
• Øksendal, Bernt (2018). Introduction to stochastic control with jump diffusions and applications to finance.
• Agram, Nacira & Øksendal, Bernt (2018). Correction to: Stochastic Control of Memory Mean-Field Processes. Applied Mathematics and Optimization. ISSN 0095-4616. 79(1), p. 205–206. doi: 10.1007/s00245-018-9483-z. Full text in Research Archive
• Øksendal, Bernt (2017). Optimal control of mean-field systems with memory.
• Øksendal, Bernt (2017). Optimal control of mean-field systems with memory.
• Øksendal, Bernt & Sulem, Agnès (2015). Applications of stochastic analysis. In Higham, Nicholas J. (Eds.), The Princeton Companion to Applied Mathematics. Princeton University Press. ISSN 978-0-691-15039-0. p. 319–327.
• Dahl, Kristina Rognlien & Øksendal, Bernt (2015). Singular recursive utility.
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2014). A comparison theorem for backward SPDEs with jumps.
• Øksendal, Bernt; Sulem, Agnès & Zhang, Tusheng (2014). A comparison theorem for backward SPDEs with jumps.
• Dahl, Kristina Rognlien; Øksendal, Bernt; Røse, Elin Engen & Mohammed, Salah-Eldin (2014). Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives.
• Aase, Knut Kristian & Øksendal, Bernt (2019). Strategic Insider Trading in Continuous Time: A New Approach. Norges Handelshøyskole. Institutt for foretaksøkonomi. ISSN 1500-4066. Show summary

  The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized by allowing time-varying noise trading. From rather simple assumptions we are able to derive the optimal trade for an insider; the trading intensity satisfies a deterministic integral equation, given perfect inside information, which we give a closed form solution to. We use a new technique called forward integration in order to find the optimal trading strategy. This is an extension of the stochastic integral which takes account of the informational asymmetry inherent in this problem. The market makers' price response is found by the use of filtering theory. The novelty is our approach, which could be extended in scope.

• Aase, Knut Kristian & Øksendal, Bernt (2019). Strategic Insider Trading Equilibrium with a non-fiduciary market maker. Norges Handelshøyskole. Institutt for foretaksøkonomi. ISSN 1500-4066. Show summary

  The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setting a modest fee conditional of the order ow, the market maker is able to obtain a profit of the order of magnitude, and even better than, a perfectly informed insider. Our model also indicates why speculative prices are more volatile than predicted by fundamentals.

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