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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 |

### Keywords:

dynamic programming; Hamilton-Jacobi-Bellman equation; interval cost function; stochastic differential equation; stochastic optimal control; uncertainty
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\textit{M. R. Bahrmand} et al., Taiwanese J. Math. 27, No. 2, 401--416 (2023; Zbl 1518.93152)

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### References:

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