Controlling a two-dimensional diffusion process at most until a fixed time

Abstract

Let be a degenerate controlled two-dimensional diffusion process such that the derivative of is a deterministic function of and . The problem of optimally controlling until time , where is the first passage time of the process to zero and is a fixed constant, is considered. The optimal control is obtained explicitly in an interesting particular case.

Keywords:

• LQG homing
• Kolmogorov backward equation
• wear process
• hitting time

AMS Subject Classification:

• 93E20

Acknowledgments

The author is grateful to the reviewers for their constructive comments.