Journal of Optimization Theory and Applications

, Volume 141, Issue 3, pp 677–700

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



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.


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


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesShandong Normal UniversityJinanPeople’s Republic of China
  2. 2.School of MathematicsShandong UniversityJinanPeople’s Republic of China

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