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A maximum principle for partial information backward stochastic control problems with applications. (English) Zbl 1203.49037

Summary: This paper studies the partial information control problems of backward stochastic systems. There are three major contributions made in this paper: (i) First, we obtain a new stochastic maximum principle for partial information control problems. Our method relies on a direct calculation of the derivative of the cost functional. (ii) Second, we introduce two classes of partial information linear-quadratic backward control problems for the first time and then investigate them using the maximum principle. Complete and explicit solutions are obtained in terms of some forward and backward stochastic differential filtering equations. (iii) Last but not least, we study a class of full information stochastic pension fund optimization problems which can be viewed as a special case of our general partial information ones. Applying the aforementioned maximum principle, we derive the optimal contribution policy in closed-form and present some related economic remarks.

MSC:

49K45 Optimality conditions for problems involving randomness
93E11 Filtering in stochastic control theory
93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91G80 Financial applications of other theories
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