The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ��1, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.
Abstract The problem of optimally controlling a standard Brownian motion until a fixed final time is considered in the case when the final cost function is an even function. Two particular problems are solved explicitly. Moreover, the best constant control as well as the best linear control are also obtained in these two particular cases.