An optimal control problem for a wiener process with random infinitesimal mean

We consider a stochastic optimal control problem for one-dimensional diffusion processes with random infinitesimal mean and variance that depend on a continuoustime Markov chain. The process is controlled until it reaches either end of an interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost. A particular case with a Wiener process will be treated in detail. Approximate and numerical solutions will be presented.

Uncontrolled Keywords

• homing problem
• Kolmogorov backward equation
• similarity solution
• Brownian motion