# A recursive algorithm for selling at the ultimate maximum in regime-switching models

## TL;DR

This paper introduces a recursive algorithm to compute the optimal stopping value in regime-switching models, enabling analysis of complex boundary functions without relying on Volterra integral equations.

## Contribution

It presents a novel recursive numerical method for optimal stopping problems in regime-switching models, especially when boundary functions are non-monotone.

## Key findings

- Effective computation of optimal stopping boundaries in complex regimes
- Applicable to models with mixed-sign drifts and non-monotone boundaries
- Provides a practical alternative to integral equation approaches

## Abstract

We propose a recursive algorithm for the numerical computation of the optimal value function $\inf_{t\le\tau\le T} E \Big[\sup_{0\le s\le T } Y_s / Y_{\tau} \big| {\cal F}_t\Big]$ over the stopping times $\tau$ with respect to the filtration of a geometric Brownian motion $Y_t$ with Markovian regime switching. This method allows us to determine the boundary functions of the optimal stopping set when no associated Volterra integral equation is available. It applies in particular when regime-switching drifts have mixed signs, in which case the boundary functions may not be monotone.