Constrained Stochastic Recursive Linear Quadratic Optimal Control Problems and Application to Finance  

作　　者：Liang-quan ZHANG Qing ZHOU 

机构地区：[1]School of Mathematics,Renmin University of China,Beijing 100872,China [2]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期375-399,共25页应用数学学报(英文版)

基　　金：financial support partly by the National Nature Science Foundation of China(Grant No.12171053,11701040,11871010&61871058);the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China(No.23XNKJ05);the financial support partly by the National Nature Science Foundation of China(Grant No.11871010,11971040);the Fundamental Research Funds for the Central Universities(No.2019XD-A11).

摘　　要：In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.

关 键 词：efficient portfolio forward-backward stochastic differential equations mean-variance portfolio selection Riccati equation recursive utilities stochastic linear quadratic optimal control 

分 类 号：O211[理学—概率论与数理统计]