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

G. C. Wang () and Z. Wu ()
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G. C. Wang: Shandong Normal University
Z. Wu: Shandong University

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 3, No 11, 677-700

Abstract: 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 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9484-1

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