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

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Lishang Jiang

Tongji University - Institute of Mathematics

Peifan Li

affiliation not provided to SSRN

Fahuai Yi

South China Normal University - Department of Math

Date Written: Oct 4, 2007

Abstract

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

Suggested Citation

Dai, Min and Jiang, Lishang and Li, Peifan and Yi, Fahuai, Finite Horizon Optimal Investment and Consumption with Transaction Costs (Oct 4, 2007). SIAM Journal on Control and Optimization, Vol. 48, No. 2, pp. 1134-1154, 2009 . Available at SSRN: https://ssrn.com/abstract=1518174 or http://dx.doi.org/10.2139/ssrn.1518174

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Lishang Jiang

Tongji University - Institute of Mathematics ( email )

1239 Siping Road
Shanghai, 200092
China

Peifan Li

affiliation not provided to SSRN ( email )

Fahuai Yi

South China Normal University - Department of Math ( email )

Guangzhou, 510631
China

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