Uncertain optimal control problem with the first hitting time objective and application to a portfolio selection model

Abstract

This paper discusses an uncertain time optimal control problem by considering time efficiency, which is to optimize the objective function about the first hitting time subject to uncertain differential equations. According to the definition of the α-path, the uncertain time optimal control problem is transformed into an equivalent deterministic optimal control problem. Two kinds of time optimal control models are presented where optimistic value and reaching index are chosen as the optimality criteria, respectively. Applying the proposed uncertain optimal control model to a portfolio selection problem, we obtain the uncertainty distribution of the first hitting time (the investors’ first profit time). Meanwhile, sufficient conditions of the optimal control strategy of such models are provided. Numerical simulations are provided which reveal the change for our optimal control strategy.