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A Malliavin Calculus Approach to General Stochastic Differential Games with Partial Information

  • An Ta Thi Kieu
  • Bernt ØksendalEmail author
  • Yeliz Yolcu Okur
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

In this article, we consider stochastic differential game where the state process is governed by a controlled Itô–Lévy process and the information available to the controllers is possibly less than the general information. All the system coefficients and the objective performance functional are assumed to be random. We use Malliavin calculus to derive a maximum principle for the optimal control of such problem. The results are applied to solve a worst-case scenario portfolio problem in finance.

Keywords

Malliavin calculus Stochastic differential game Stochastic control, Jump diffusion Partial information Optimal worst-case scenario portfolio 

Notes

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ ERC grant agreement no [228087].

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • An Ta Thi Kieu
    • 1
  • Bernt Øksendal
    • 1
    Email author
  • Yeliz Yolcu Okur
    • 2
  1. 1.Center of Mathematics for Applications (CMA)University of OsloBlindernNorway
  2. 2.Institute of Applied MathematicsMiddle East Technical Unoversity (METU)AnkaraTurkey

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