Article

Journal of Optimization Theory and Applications

, Volume 141, Issue 3, pp 677-700

First online:

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

  • G. C. WangAffiliated withSchool of Mathematical Sciences, Shandong Normal University
  • , Z. WuAffiliated withSchool of Mathematics, Shandong University Email author 

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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.

Keywords

Risk-sensitive optimal control General maximum principle Partial information Nonzero sum differential game Portfolio choices