Non-homogeneous stochastic LQ control with regime switching and random coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-05 DOI:10.3934/mcrf.2023021

Ying Hu, Xiaomin Shi, Z. Xu

引用次数: 0

Abstract

This paper is concerned with a general non-homogeneous stochastic linear quadratic (LQ) control problem with regime switching and random coefficients. We obtain the explicit optimal state feedback control and optimal value for this problem in terms of two systems of backward stochastic differential equations (BSDEs): one is the famous stochastic Riccati equation and the other one is a new linear multi-dimensional BSDE with all coefficients being unbounded. The existence and uniqueness of the solutions to these two systems of BSDEs are proved by means of BMO martingales and contraction mapping method. At last, the theory is applied to study an asset-liability management problem under the mean-variance criteria.

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具有状态切换和随机系数的非齐次随机LQ控制

研究一类一般的带状态切换和随机系数的非齐次随机线性二次控制问题。本文利用两种后向随机微分方程(BSDEs)系统:一种是著名的随机Riccati方程，另一种是一种新的所有系数无界的线性多维BSDE系统，得到了该问题的显式最优状态反馈控制和最优值。利用BMO鞅和收缩映射方法证明了这两类BSDEs系统解的存在唯一性。最后，应用该理论研究了均值-方差准则下的资产负债管理问题。

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

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.