AN ANALYTIC RECURSIVE METHOD FOR OPTIMAL MULTIPLE STOPPING: CANADIZATION AND PHASE-TYPE FITTING

Tim Leung, Kazutoshi Yamazaki () and Hongzhong Zhang ()
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Kazutoshi Yamazaki: Department of Mathematics, Kansai University, Osaka, Japan
Hongzhong Zhang: Statistics Department, Columbia University, New York, NY 10027, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 05, 1-31

Abstract: We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Lévy 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 Lévy 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 independent, identically distributed 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 Lévy 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; refraction times; maturity randomization; phase-type fitting; Lévy processes (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (13)

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Working Paper: An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting (2015)
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DOI: 10.1142/S0219024915500326

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