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

## TL;DR

This paper introduces and solves a recursive class of optimal stopping problems, with applications to stock trading, demonstrating existence, uniqueness, and optimal strategies in multi-dimensional Markovian models.

## Contribution

It develops a framework for recursive optimal stopping problems where the payoff depends on the value function itself, and applies it to stock trading models.

## Key findings

- Existence and uniqueness of the value function as a fixed point.
- Derivation of optimal stopping rules in stock trading models.
- Application to multi-venue stock trading scenarios.

## 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.