Abstract
This paper is concerned with the Dynkin game (a zero-sum optimal stopping game). The dynamic of the system is modeled by a regime switching diffusion, in which the regime switching mechanism provides the structural changes of the random environment. The goal is to find a saddle point for the payoff functional up to one of the players exiting the game. Taking advantage of the method of penalization and the dynamic programming principle, the value function of the game problem is shown to be the unique viscosity solution to the associated variational inequalities. We also consider a financial example of pricing game option under a regime switching market. Both optimal stopping rules for the buyer and the seller and fair price of the option are numerically demonstrated in this example. All the results are markedly different from the traditional cases without regime switching.
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This work was supported by the National Natural Science Foundation of China (11801072, 11831010, 61961160732), the Natural Science Foundation of Jiangsu Province, China (BK20180354), the Natural Science Foundation of Shandong Province, China (ZR2019ZD42), and the Simons Foundation’s Collaboration Grant for Mathematicians (235179).
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Lv, S., Wu, Z. & Zhang, Q. The Dynkin game with regime switching and applications to pricing game options. Ann Oper Res 313, 1159–1182 (2022). https://doi.org/10.1007/s10479-020-03656-y
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DOI: https://doi.org/10.1007/s10479-020-03656-y