Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem

31 Pages Posted: 12 Dec 2005

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Fahuai Yi

South China Normal University - Department of Math

Date Written: January 2006

Abstract

This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well developed theory of variational inequality to study the problem. The $C^{2,1}$ regularity of the value function is proven and the optimal investment policies are completely characterized. Relying on the double obstacle problem, we extend the binomial method widely used in option pricing to determine the optimal investment policies. Numerical examples are presented as well.

Keywords: optimal investment, transaction costs, finite horizon, double obstacle problem, stochastic control, Riccati equation, portfolio selection, free boundary

Suggested Citation

Dai, Min and Yi, Fahuai, Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem (January 2006). Available at SSRN: https://ssrn.com/abstract=868499 or http://dx.doi.org/10.2139/ssrn.868499

Min Dai (Contact Author)

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

Singapore

Fahuai Yi

South China Normal University - Department of Math ( email )

Guangzhou, 510631
China

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