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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical 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。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.