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

Min Dai, Yifei Zhong
2008 Social Science Research Network  
This paper is concerned with numerical solutions to a singular stochastic control problem arising from the 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
more » ... 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 behaviour of the optimal trading strategy. . Dai would like to thank his students Joline A.V. Uichanco and Kaiyun Chong for parts of numerical implementation. He also thanks Yue-Kuen Kwok and Xingye Yue for helpful comments and an anonymous referee for valuable suggestions.
doi:10.2139/ssrn.1210105 fatcat:tn3bcbjwhbeqdjifyvurmhghwa