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Journal of Optimization Theory and Applications

, Volume 160, Issue 1, pp 302–343 | Cite as

Stochastic Differential Games in Insider Markets via Malliavin Calculus

  • O. Menoukeu PamenEmail author
  • F. Proske
  • H. Binti Salleh
Article

Abstract

In this paper, we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider.

Keywords

Malliavin calculus Maximum principle Jump diffusion Stochastic control Insider information Stochastic differential game 

Notes

Acknowledgements

The authors are grateful to two anonymous referees and Professor Franco Giannessi for their helpful comments and suggestions.

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

  • O. Menoukeu Pamen
    • 1
    Email author
  • F. Proske
    • 2
  • H. Binti Salleh
    • 3
  1. 1.Institute for Financial and Actuarial Mathematics, Department of MathematicsUniversity of LiverpoolLiverpoolUK
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Department of MathematicsUniversiti Malaysia TerengganuKuala TerengganuMalaysia

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