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General Maximum Principles for Partially Observed Risk-Sensitive Optimal Control Problems and Applications to Finance

Author

Listed:
  • G. C. Wang

    (Shandong Normal University)

  • Z. Wu

    (Shandong University)

Abstract

This paper is concerned with partially observed risk-sensitive optimal control problems. Combining Girsanov’s theorem with a standard spike variational technique, we obtain some general maximum principles for the aforementioned problems. One of the distinctive differences between our results and the standard risk-neutral case is that the adjoint equations and variational inequalities strongly depend on a risk-sensitive parameter γ. Two examples are given to illustrate the applications of the theoretical results obtained in this paper. As a natural deduction, a general maximum principle is also obtained for a fully observed risk-sensitive case. At last, this result is applied to study a risk-sensitive optimal portfolio problem. An explicit optimal investment strategy and a cost functional are obtained. A numerical simulation result shows the influence of a risk-sensitive parameter on an optimal investment proportion; this coincides with its economic meaning and theoretical results.

Suggested Citation

  • G. C. Wang & Z. Wu, 2009. "General Maximum Principles for Partially Observed Risk-Sensitive Optimal Control Problems and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 677-700, June.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:3:d:10.1007_s10957-008-9484-1
    DOI: 10.1007/s10957-008-9484-1
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    Cited by:

    1. Peng Wang, 2023. "Risk-Sensitive Maximum Principle for Controlled System with Delay," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    2. Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.

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