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Maximum principle of optimal stochastic control with terminal state constraint and its application in finance. (English) Zbl 1401.93235

Summary: This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland’s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.

MSC:

93E20 Optimal stochastic control
91G80 Financial applications of other theories
91G10 Portfolio theory
49K45 Optimality conditions for problems involving randomness
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