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An explicit solution to an optimal stopping problem with regime switching

Part of: Sequential methods Stochastic processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Xin Guo
Xin Guo*
Affiliation:
IBM Research Division and University of Alberta
*
∗ Postal address: T. J. Watson Research Center, P.O. Box 218, IBM, Yorktown Heights, NY 10598, USA. Email address: [email protected]
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Abstract

We investigate an optimal stopping time problem which arises from pricing Russian options (i.e. perpetual look-back options) on a stock whose price fluctuations are modelled by adjoining a hidden Markov process to the classical Black-Scholes geometric Brownian motion model. By extending the technique of smooth fit to allow jump discontinuities, we obtain an explicit closed-form solution. It gives a non-standard application of the well-known smooth fit principle where the optimal strategy involves jumping over the optimal boundary and by an arbitrary overshoot. Based on the optimal stopping analysis, an arbitrage-free price for Russian options under the hidden Markov model is derived.

Keywords

hidden Markov processmartingaleoptimal stoppingregime switchingRussian options

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 62L10: Sequential analysis 93E20: Optimal stochastic control
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 464 - 481
Copyright
Copyright © Applied Probability Trust 2001 

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