Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
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Penalty methods for continuous-time portfolio selection with proportional transaction costs
Min Dai, Yifei Zhong
Abstract
ABSTRACT
This paper is concerned with numerical solutions to a singular stochastic control problem arising from continuous-time portfolio selection with proportional transaction costs. 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 a finite difference discretization. Convergence analysis is presented. We also show that the standard penalty method can be applied in the case of a 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 behavior of the optimal trading strategy.
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