Finite Horizon Optimal Investment and Consumption with Transaction Costs

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 Stu...

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Vydané v:SIAM journal on control and optimization Ročník 48; číslo 2; s. 1134 - 1154
Hlavní autori: Dai, Min, Jiang, Lishang, Li, Peifan, Yi, Fahuai
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Predmet:
Consumption
Costs
Financing
Free boundaries
Horizon
Investment
Investment policy
Mathematical analysis
Optimization
Risk aversion
Stochastic control theory
Strategy
Studies
Transaction costs
ISSN:0363-0129, 1095-7138
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Shrnutí: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. [PUBLICATION ABSTRACT]
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ISSN:0363-0129
1095-7138
DOI:10.1137/070703685