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A Stochastic HJB Equation for Optimal Control of Forward-Backward SDEs

In: The Fascination of Probability, Statistics and their Applications

Author

Listed:
  • Bernt Øksendal

    (University of Oslo, Blindern, Department of Mathematics
    Norwegian School of Economics)

  • Agnès Sulem

    (University of Oslo, Blindern, Department of Mathematics
    INRIA Paris-Rocquencourt
    Université Paris-Est)

  • Tusheng Zhang

    (University of Manchester, School of Mathematics)

Abstract

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.

Suggested Citation

  • Bernt Øksendal & Agnès Sulem & Tusheng Zhang, 2016. "A Stochastic HJB Equation for Optimal Control of Forward-Backward SDEs," Springer Books, in: Mark Podolskij & Robert Stelzer & Steen Thorbjørnsen & Almut E. D. Veraart (ed.), The Fascination of Probability, Statistics and their Applications, pages 435-446, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-25826-3_20
    DOI: 10.1007/978-3-319-25826-3_20
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