A numerical scheme for a singular control problem: Investment-consumption under proportional transaction costs

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:333

Article

Tsai, Wan-Yu¹  Fahim, Arash¹ 

[1] Florida State Univ, Dept Math, 1017 Acad Way, Tallahassee, FL 32306 USA

关键词: Hamilton-Jacobi-Bellman equation;    Stochastic control;    Monte Carlo approximation;    Backward stochastic differential equations;    Portfolio optimization;    Transaction costs;   

DOI  :  10.1016/j.cam.2017.10.035

来源: Elsevier

【 摘 要 】

This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider optimal allocation of wealth among multiple stocks and a bank account in order to maximize the finite horizon discounted utility of consumption. The problem is mainly governed by a time-dependent Hamilton-Jacobi-Bellman equation with gradient constraints. We propose a numerical method which is composed of Monte Carlo simulation to take advantage of the high-dimensional properties and finite difference method to approximate the gradients of the value function. Numerical results illustrate behaviors of the optimal trading strategies and also satisfy all qualitative properties proved in Dai et al. (2009) and Chen and Dai (2013). (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free