First-hitting Place Optimization Problems for Two-dimensional Degenerate Diffusion Processes

Optimal control problems for degenerate two-dimensional diffusion processes are considered. The processes could serve as models for wear processes. The objective is to make the controlled process leave the continuation region through a given part of the boundary. Explicit and exact solutions are obtained for important processes such as the geometric Brownian motion and the Ornstein-Uhlenbeck process.

Mots clés

• Wear processes
• Kolmogorov backward equation
• homing problem
• dynamic programming
• special functions
• geometric Brownian motion
• Ornstein-Uhlenbeck process