Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations Research Pub Date : 2024-07-29 DOI:10.1287/moor.2023.0123

José Luis Pérez, Neofytos Rodosthenous, Kazutoshi Yamazaki

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引用次数: 0

Abstract

We introduce a new nonzero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modeling the value of an asset, one player observes and can act on the process continuously, whereas the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, whereas the other one gets nothing. We study how each player balances the maximization of gains against the maximization of the likelihood of stopping before the opponent. In such a setup driven by a Lévy process with positive jumps, we not only prove the existence but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behavior of the players’ strategies as well as the quantification of the value of available exercise opportunities.Funding: K. Yamazaki was partly supported by The Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) [Grants 19H01791, 20K03758, and 24K06844], Open Partnership Joint Research Projects [Grant JPJSBP120209921], and the University of Queensland [start-up grant].

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连续锻炼机会与定期锻炼机会的非零和最优停止博弈

我们引入了一种新的非零和博弈，即具有不对称执行机会的最优止损博弈。给定一个模拟资产价值的随机过程，其中一个博弈方可以持续观察并对该过程采取行动，而另一个博弈方只能在独立的泊松到达时间周期性地对该过程采取行动。最先停止的一方会获得奖励，每个玩家的奖励都不同，而另一方则什么也得不到。我们将研究每个棋手如何在收益最大化和先于对手停止的可能性最大化之间取得平衡。在这种由具有正跳跃的莱维过程驱动的情况下，我们不仅证明了纳什均衡的存在，还明确地构建了一个纳什均衡，其博弈值用规模函数来表示。我们还提供了看跌期权报酬的数值示例，以研究博弈者的策略行为以及可用行权机会价值的量化：K. Yamazaki 部分获得日本学术振兴会（JSPS）科学研究补助金（KAKENHI）[19H01791、20K03758 和 24K06844 号补助金]、开放合作伙伴联合研究项目[JPJSBP120209921 号补助金]以及昆士兰大学[启动补助金]的资助。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.