A class of recursive optimal stopping problems with applications to stock trading

Abstract

In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem is well posed, in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues and we determine the optimal stopping rule in that case.

arXiv comment36 pages, 2 figures. In this version, we provide a general analysis of a class of recursive optimal stopping problems with both finite-time and infinite-time horizon. We also discuss other applications and provide a comparison with a non-recursive model