Finite Horizon Optimal Investment and Consumption with Transaction Costs
SIAM Journal on Control and Optimization, Vol. 48, No. 2, pp. 1134-1154, 2009
20 Pages Posted: 8 Dec 2009
Date Written: Oct 4, 2007
This paper concerns continuous-time optimal investment and consumption decision of a CRRA investor who faces proportional transaction costs and finite time horizon. In the no consumption case, it has been studied by Liu and Loewenstein (2002) and Dai and Yi (2006). 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 to the present problem.
Keywords: optimal investment and consumption, transaction costs, finite horizon, free boundaries, variational inequality, gradient constraints, singular stochastic control
JEL Classification: G11
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