简短交流：离散时间中马尔可夫均衡控制的存在性

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2023-12-08 DOI:10.1137/23m1594121

Erhan Bayraktar, Bingyan Han

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 14 卷第 4 期，第 SC60-SC71 页，2023 年 12 月。摘要。Björk 和 Murgoci [Finance Stoch.如果目标在每个时间步中都是 inf-compact 的，那么就存在一个非随机的 Borel 可测马尔可夫均衡策略。我们提供了一个充分条件，即在给定状态下，成本为下半连续且自下而上有界，过渡核在控制中为连续的，则下紧凑性进而存在。控制空间不必紧凑。

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Short Communication: Existence of Markov Equilibrium Control in Discrete Time

SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC60-SC71, December 2023.
Abstract. For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Björk and Murgoci [Finance Stoch., 18 (2014), pp. 545–592] is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium policy exists if the objective is inf-compact in every time step. We provide a sufficient condition for the inf-compactness and thus existence with costs that are lower semicontinuous and bounded from below and transition kernels that are continuous in controls under given states. The control spaces need not to be compact.

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.