A survey of numerical solutions for stochastic control problems: Some recent progress

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI:10.3934/naco.2022004

Zhu Jin, Mingxue Qiu, K. Tran, G. Yin

引用次数: 4

Abstract

This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular controls and singular controls. The main objective of this paper is to provide a survey on some recent advances on Markov chain approximation methods for solving stochastic control problems numerically. A number of applications in insurance, mathematical biology, epidemiology, and economics are presented. Several numerical examples are provided for demonstration.

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随机控制问题数值解的研究进展

本文综述了控制开关扩散数值解的一些最新进展。我们首先回顾开关扩散和控制开关扩散的基础知识。然后我们介绍了常规控件和奇异控件。本文的主要目的是综述用马尔可夫链近似方法数值求解随机控制问题的一些最新进展。它在保险、数学生物学、流行病学和经济学等领域的广泛应用。给出了几个数值算例进行论证。

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

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.