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This paper concerns the numerical solution of a fully nonlinear parabolicdouble obstacle problem arising from a finite portfolio selection withproportional transaction costs. We consider the optimal allocation of wealthamong multiple stocks and a bank account in order to maximize the finitehorizon discounted utility of consumption. The problem is mainly governed by atime-dependent Hamilton-Jacobi-Bellman equation with gradient constraints. Wepropose a numerical method which is composed of Monte Carlo simulation to takeadvantage of the high-dimensional properties and finite difference method toapproximate the gradients of the value function. Numerical results illustratebehaviors of the optimal trading strategies and also satisfy all qualitativeproperties proved in Dai et al. (2009) and Chen and Dai (2013).

A Numerical Scheme for A Singular control problem: Investment-Consumption Under Proportional Transaction Costs