Abstract
A stochastic optimal problem of the regulator type is considered, where the stopping time of the process is a random variable to be selected in addition to control variables.
We rigorously derived a nonlinear equation which is satisfied by the optimum cost function. Since this equation has not a unique solution in general, computing algorithms for the optimum cost function are concerned with. With the aid of the optimal stopping theory, the optimum cost function is characterized as the maximal or minimal solution of the equation under certain conditions. And on this basis, it is pointed out that a recurrent equation generates a converging series to the desired function when some initial function is adopted.
A linear-quadratic-Gaussian case is discussed as an example.
