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SELLING AT THE ULTIMATE MAXIMUM IN A REGIME-SWITCHING MODEL

School of Finance and Economics, Jiangsu University, Zhenjiang 212013, P. R. China

and

School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore

E-mail Address: nprivault@ntu.edu.sg

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https://doi.org/10.1142/S0219024917500182Cited by:6 (Source: Crossref)

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 [du Toit & Peskir (2009) Selling a stock at the ultimate maximum, Annals of Applied Probability19 (3), 983–1014.] in the classical Brownian case.

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