Constructing time-homogeneous generalized diffusions consistent with optimal stopping values

Abstract

Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the problem value in this setting. In this article we consider an inverse problem; given the set of problem values for a family of objective functions, we aim to recover the diffusion. Under a natural assumption on the family of objective functions, we can characterize the existence and uniqueness of a diffusion for which the optimal stopping problems have the specified values. The solution of the problem relies on techniques from generalized convexity theory.

Keywords:

• optimal stopping
• generalized convexity
• generalized diffusions
• inverse American option problem

Acknowledgement

DGH would like to thank Nizar Touzi for suggesting generalized convexity as an approach for this problem.

Notes

1. [email protected]

Additional information

Notes on contributors

Martin Klimmek

1 1. [email protected]