An Analytic Recursive Method for Optimal Multiple Stopping: Canadization and Phase-Type Fitting

30 Pages Posted: 19 Apr 2014 Last revised: 28 Oct 2015

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Kazutoshi Yamazaki

Kansai University - Department of Mathematics

Hongzhong Zhang

Columbia University

Date Written: May 28, 2015

Abstract

We study an optimal multiple stopping problem driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence the solutions in general cannot be attained analytically. Motivated by the maturity randomization (Canadization) technique by Carr (1998), we approximate the refraction times by i.i.d. Erlang random variables. In addition, fitting random jumps to phase-type distributions, our method involves repeated integrations with respect to the resolvent measure written in terms of the scale function of the underlying Levy process. We derive a recursive algorithm to compute the value function in closed form, and sequentially determine the optimal exercise thresholds. A series of numerical examples are provided to compare our analytic formula to results from Monte Carlo simulation.

Keywords: optimal multiple stopping, Levy process, maturity randomization, refraction times, phase-type fitting

JEL Classification: C60, C63

Suggested Citation

Leung, Tim and Yamazaki, Kazutoshi and Zhang, Hongzhong, An Analytic Recursive Method for Optimal Multiple Stopping: Canadization and Phase-Type Fitting (May 28, 2015). International Journal of Theoretical and Applied Finance, vol. 18, issue 5, p.1550032, 2015, Available at SSRN: https://ssrn.com/abstract=2426430 or http://dx.doi.org/10.2139/ssrn.2426430

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Kazutoshi Yamazaki

Kansai University - Department of Mathematics ( email )

3-3-35 Yamate-cho, Suita-shi
Osaka, 564-8680
Japan

HOME PAGE: http://https://sites.google.com/site/kyamazak/

Hongzhong Zhang

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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