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.


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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