Selling at the ultimate maximum in a regime switching model

TL;DR

This paper develops optimal stopping strategies for predicting maximum values in a regime-switching model driven by a Markov chain, extending classical Brownian motion results using PDE methods.

Contribution

It introduces regime-dependent optimal stopping rules and continuity properties, replacing closed-form solutions with PDE-based analysis in a more complex setting.

Findings

Derived regime-specific optimal stopping strategies

Proved continuity of value and boundary functions

Extended classical results to Markov regime-switching models

Abstract

This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current regime state, and prove a number of continuity properties relating to optimal value and boundary functions. Our approach replaces the use of closed form expressions, which are not available in our setting, with PDE arguments that also simplify the approach of [2] in the classical Brownian case.