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
Date Written: May 27, 2015
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
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