FINITE HORIZON OPTIMAL INVESTMENT AND CONSUMPTION WITH TRANSACTION COSTS

被引：41

作者：

Dai, Min ^{[1
]}

Jiang, Lishang ^{[2
]}

Li, Peifan ^{[1
]}

Yi, Fahuai ^{[3
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117548, Singapore

[2] Tongji Univ, Dept Appl Math, Shanghai 200092, Peoples R China

[3] S China Normal Univ, Dept Math, Guangzhou, Guangdong, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 48卷 / 02期

关键词：

optimal investment and consumption; transaction costs; finite horizon; free boundaries; variational inequality; gradient constraints; singular stochastic control; SINGULAR STOCHASTIC-CONTROL; PORTFOLIO SELECTION; MODEL;

D O I：

10.1137/070703685

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper concerns continuous-time optimal investment and the consumption decision of a constant relative risk aversion (CRRA) investor who faces proportional transaction costs and a finite time horizon. In the no-consumption case, it has been studied by Liu and Loewenstein [Review of Financial Studies, 15 (2002), pp. 805-835] and Dai and Yi [J. Differential Equations, 246 (2009), pp. 1445-1469]. Mathematically, it is a singular stochastic control problem whose value function satisfies a parabolic variational inequality with gradient constraints. The problem gives rise to two free boundaries which stand for the optimal buying and selling strategies, respectively. We present an analytical approach to analyze the behaviors of free boundaries. The regularity of the value function is studied as well. Our approach is essentially based on the connection between singular control and optimal stopping, which is first revealed in the present problem.

引用

页码：1134 / 1154

页数：21

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