Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models

SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 2373–2405, 2015

25 Pages Posted: 14 Feb 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 27, 2015

Abstract

This paper studies a class of optimal multiple stopping problems driven by Levy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount factor. Moreover, successive exercise opportunities are separated by i.i.d. random refraction times. Under a wide class of two-sided Levy models with a general random refraction time, we rigorously show that the optimal strategy to exercise successive call options is uniquely characterized by a sequence of up-crossing times. The corresponding optimal thresholds are determined explicitly in the single stopping case and recursively in the multiple stopping case.

Keywords: optimal multiple stopping, negative discount rate, random refraction times, Levy processes, stock loan, real option

JEL Classification: G32, D81, C61

Suggested Citation

Leung, Tim and Yamazaki, Kazutoshi and Zhang, Hongzhong, Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models (May 27, 2015). SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 2373–2405, 2015 , Available at SSRN: https://ssrn.com/abstract=2395256 or http://dx.doi.org/10.2139/ssrn.2395256

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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