Skip to main content
SpringerLink
Log in

Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward Stochastic Differential Equations with Application

  • Published:
Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

Abstract

This paper studies the risk-sensitive optimal control problem for a backward stochastic system. More precisely, we set up a necessary stochastic maximum principle for a risk-sensitive optimal control of this kind of equations. The control domain is assumed to be convex and the generator coefficient of such system is allowed to be depend on the control variable. As a preliminary step, we study the risk-neutral problem for which an optimal solution exists. This is an extension of initial control system to this type of problem, where the set of admissible controls is convex. An example to carried out to illustrate our main result of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Djehiche, B., Tembine, H., Tempone, R.: A stochastic maximum principle for risk-sensitive mean-field type control. IEEE Trans. Autom. Control 60(10), 2640–2649 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • El-Karoui, N., Hamadène, S.: BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations. Stoch. Process. Appl. 107, 145–169 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Lim, A.E.B., Zhou, X.: A new risk-sensitive maximum principle. IEEE Trans. Autom. Control 50(7), 958–966 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14(1–2), 61–74 (1990)

    MathSciNet  MATH  Google Scholar 

  • Shi, J., Wu, Z.: A risk-sensitive stochastic maximum principle for optimal control of jump diffusions and its applications. Acta Math. Sci. 31(2), 419–433 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Shi, J., Wu, Z.: Maximum principle for risk-sensitive stochastic optimal control problem and applications to finance. Stoch. Anal. Appl. 30(6), 997–1018 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Tembine, H., Zhu, Q., Basar, T.: Risk-sensitive mean-field games. IEEE Trans. Autom. Control 59(4), 835–850 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Yong, J.: Optimality variational principle for controlled forward-backward stochastic differential equations with mixed initial-terminal conditions. Siam J. Control Optim. 48(06), 4119–4156 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Applied Mathematics, Mohamed Khider University, P.O. Box 145, 07000, Biskra, Algeria

    Adel Chala

Authors
  1. Adel Chala
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adel Chala.

Additional information

This work is Partially supported by The CNEPRU project N: C00L03UN070120140029.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chala, A. Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward Stochastic Differential Equations with Application. Bull Braz Math Soc, New Series 48, 399–411 (2017). https://doi.org/10.1007/s00574-017-0031-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-017-0031-2

Keywords

Mathematics Subject Classification

Search

Navigation