Optimal Selling Strategies under Regime-Switching Market Environment with Finite Expiry

Jie Xing,Taoshun He,Xiaohua Ding

doi:10.1155/2021/5920285

Abstract

This paper addresses an optimal stock liquidation problem over a finite-time horizon; to that end, we model it as an optimal stopping problem in a regime-switching market. The optimal stopping time is written as a solution to a system of Volterra type integral equations. Moreover, it reveals that when the risk-free interest rate is always lower than the return rate of the stock, it is never optimal to sell the stock early; otherwise, one should sell the stock in bear market if the stock price reaches a critical value and hold the stock in bull market until the maturity date. Finally, we present a trinomial tree method for numerical implementation. The numerical results are consistent with the theoretical findings.

Highlights

“What is the best time to sell an asset to maximize revenue?” is a fundamental problem in finance
This paper is concerned with the optimal selling strategies. at is, we mainly focus on the early exercise boundary with respect to the optimal stopping problem rather than the value function
Jacka and Ocejo studied the regularity of the value function for a finite horizontal optimal stopping problem in the presence of regime-switching uncertainty [12]. e abovementioned authors mainly concentrated on the value function and did not investigate the free boundary arising from American option pricing problem

Summary

Introduction

“What is the best time to sell an asset to maximize revenue?” is a fundamental problem in finance. E finite horizontal optimal selling rule under regime-switching model was firstly studied by Pemy and Zhang using viscosity solution approach [7]. It is known that Pemy and Zhang only discussed the value function to the related HJB equation, and up to the Discrete Dynamics in Nature and Society author’s knowledge, the optimal selling strategies under regime-switching model are still unknown so far [7]. In filling this gap, this paper is concerned with the optimal selling strategies.

Problem Set-Up

Main Results

Numerical Examples

Conclusions

Proof of Lemma 1

Proof of Lemma 2