Download this Paper Open PDF in Browser

Multi-dimensional Portfolio Optimization with Proportional Transaction Costs

32 Pages Posted: 13 Jul 2004  

Kumar Muthuraman

University of Texas at Austin - McCombs School of Business

Sunil Kumar

Independent

Date Written: October 2004

Abstract

We provide a computational study of the problem of optimally allocating wealth among multiple stocks and a bank account, in order to maximize the infinite horizon discounted utility of consumption. We consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. Our model allows for correlation between the price processes, which in turn gives rise to interesting hedging strategies. This results in a stochastic control problem with both drift-rate and singular controls, that can be recast as a free boundary problem in partial differential equations. Adapting the finite element method and using an iterative procedure that converts the free-boundary problem into a sequence of fixed boundary problems, we provide an efficient numerical method for solving this problem. We present computational results that describe the impact of volatility, risk aversion of the investor, level of transaction costs and correlation among the risky assets on the structure of the optimal policy. Finally we suggest and quantify some heuristic approximations.

Keywords: Portfolio optimization, transaction costs, stochastic control, Hamilton-Jacobi-Bellman equation, free boundary problem

JEL Classification: G11, C61

Suggested Citation

Muthuraman, Kumar and Kumar, Sunil, Multi-dimensional Portfolio Optimization with Proportional Transaction Costs (October 2004). Available at SSRN: https://ssrn.com/abstract=563944 or http://dx.doi.org/10.2139/ssrn.563944

Kumar Muthuraman (Contact Author)

University of Texas at Austin - McCombs School of Business ( email )

Austin, TX 78712
United States

Sunil Kumar

Independent

No Address Available

Paper statistics

Downloads
488
Rank
46,976
Abstract Views
1,698