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Title: Finite horizon optimal investment and consumption with transaction costs
Authors: Min, D. 
Lishang, J.
Peifan, L.
Fahuai, Y.I.
Keywords: Finite horizon
Free boundaries
Gradient constraints
Optimal investment and consumption
Singular stochastic control
Transaction costs
Variational inequality
Issue Date: 2009
Source: Min, D., Lishang, J., Peifan, L., Fahuai, Y.I. (2009). Finite horizon optimal investment and consumption with transaction costs. SIAM Journal on Control and Optimization 48 (2) : 1134-1154. ScholarBank@NUS Repository.
Abstract: 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. © 2009 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Control and Optimization
ISSN: 03630129
DOI: 10.1137/070703685
Appears in Collections:Staff Publications

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