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A minimum principle for stochastic optimal control problem with interval cost function. (English) Zbl 1518.93152

Summary: In this paper, we study an optimal control problem in which their cost function is interval-valued. Also, a stochastic differential equation governs their state space. Moreover, we introduce a generalized version of Bellman’s optimality principle for the stochastic system with an interval-valued cost function. Also, we obtain the Hamilton-Jacobi-Bellman equations and their control decisions. Two numerical examples happen in finance in which their cost function are interval-valued functions, illustrating the efficiency of the discussed results. The obtained results provide significantly reliable decisions compared to the case where the conventional cost function is applied.

MSC:

93E20 Optimal stochastic control
49L12 Hamilton-Jacobi equations in optimal control and differential games
49L20 Dynamic programming in optimal control and differential games
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