Penalty Methods for Continuous-Time Portfolio Selection with Proportional Transaction Costs

25 Pages Posted: 7 Aug 2008

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Yifei Zhong

University of Oxford - Mathematical Institute; University of Oxford - Mathematical Institute

Date Written: August 7, 2008

Abstract

We are concerned with numerical solutions for the continuous-time portfolio selection with proportional transaction costs which is described as a singular stochastic control problem. The associated value function is governed by a variational inequality with gradient constraints. We propose a penalty method to deal with the gradient constraints and employ the finite difference discretization. Convergence analysis is presented. We also show that the standard penalty method can be applied in the case of single risky asset where the problem can be reduced to a standard variational inequality. Numerical results are given to demonstrate the efficiency of the methods and to examine the behaviors of the optimal trading strategy.

Suggested Citation

Dai, Min and Zhong, Yifei, Penalty Methods for Continuous-Time Portfolio Selection with Proportional Transaction Costs (August 7, 2008). Available at SSRN: https://ssrn.com/abstract=1210105 or http://dx.doi.org/10.2139/ssrn.1210105

Min Dai (Contact Author)

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

Singapore

Yifei Zhong

University of Oxford - Mathematical Institute ( email )

Mathematical Institute
24-29 St Giles
Oxford, Oxfordshire OX1 3LB
United Kingdom

University of Oxford - Mathematical Institute ( email )

24-29 St Giles'
Oxford, OX1 3LB
United Kingdom

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