OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS  

作　　者：罗葵 王光明 胡亦钧 

机构地区：[1]Industrial Training Centre, Shenzhen Polytechnic [2]China Merchants Bank [3]School of Mathematics and Statistics, Wuhan University

出　　处：《Acta Mathematica Scientia》2011年第2期483-490,共8页数学物理学报（B辑英文版）

基　　金：Supported in part by the National Natural ScienceFoundation of China (10671149);the Ministry of Education of China (NCET-04-0667)

摘　　要：In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi--Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal problem is derived when there is no liquidity constraint.In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi--Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal problem is derived when there is no liquidity constraint.

关 键 词：Portfolio selection wealth tracking liquidity constraints HJB equation Lagrange multiplier 

分 类 号：O224[理学—运筹学与控制论]