Optimal Stopping with Expectation Constraints

Specialeforsvar ved Kristoffer Brix

Titel: Optimal Stopping with Expectation Constraints

Abstract: We consider the problem of optimally stopping a diffusion process with a stopping time satisfying an expectation constraint. This type of problem falls outside the scope of standard optimal stopping theory. Extending the state-space to make the expectation constraint more tangible, we can transform the optimal stopping problem into an optimal control problem, whose value function may be characterized by a dynamic programming equation. When a solution to the dynamic programming equation exists, we provide a verification theorem to determine when this solution coincides with the value function. We also show, borrowing results on Skorokhod embeddings, that the problem may reduced into a linear optimization problem over a convex set of probability measures. Examples are provided throughout to show how to apply the theory.

Vejleder: Jesper Lund Pedersen
Censor: Bjarne Astrup Jensen