Local Time Pushed Mixed Equilibrium Strategies for Time-Inconsistent Stopping Problems

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-04-09 DOI:10.1137/22m1506651

Andi Bodnariu, Sören Christensen, Kristoffer Lindensjö

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1261-1290, April 2024.
Abstract. We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a nonexponential (weighted) discount function. In particular, we study (weak) equilibria for this problem in a novel class of mixed (i.e., randomized) stopping times based on a local time construction of the stopping intensity. For a general formulation of the problem we provide a verification theorem giving sufficient conditions for mixed (and pure) equilibria in terms of a set of variational inequalities, including a smooth fit condition. We apply the theory to prove the existence of (mixed) equilibria in a recently studied real options problem in which no pure equilibria exist.

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时间不一致停止问题的局部时间推动混合均衡策略

SIAM 控制与优化期刊》第 62 卷第 2 期第 1261-1290 页，2024 年 4 月。摘要。我们考虑用博弈论方法来解决一维扩散的时间不一致停止问题，其中时间不一致是由于非指数（加权）贴现函数的存在。特别是，我们基于停止强度的局部时间构造，研究了该问题在一类新型混合（即随机）停止时间中的（弱）均衡。对于问题的一般表述，我们用一组变分不等式（包括平稳拟合条件）给出了一个验证定理，给出了混合（和纯）均衡的充分条件。我们运用该理论证明了最近研究的一个不存在纯均衡的实物期权问题中（混合）均衡的存在。

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

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.