OPTIMAL MULTIPLE STOPPING WITH NEGATIVE DISCOUNT RATE AND RANDOM REFRACTION TIMES UNDER LEVY MODELS

被引:5
作者
Leung, Tim [1 ]
Yamazaki, Kazutoshi [2 ]
Zhang, Hongzhong [3 ]
机构
[1] Columbia Univ, IEOR Dept, New York, NY 10027 USA
[2] Kansai Univ, Dept Math, Osaka, Japan
[3] Columbia Univ, Dept Stat, New York, NY 10027 USA
关键词
optimal multiple stopping; negative discount rate; random refraction times; Levy processes; stock loan; PERPETUAL OPTIONS; RISK-AVERSION; STOCK-OPTIONS; VALUATION; EXERCISE; AMERICAN; LOANS;
D O I
10.1137/140957317
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 independently and identically distributed 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 upcrossing times. The corresponding optimal thresholds are determined explicitly in the single stopping case and recursively in the multiple stopping case.
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页码:2373 / 2405
页数:33
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