Article1995

OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTS

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

Abstract

We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a fixed Traction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate, so me optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as m correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optima! rule. We use numerical methods to solve for the optima! policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading.

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References

1971Optimum consumption and portfolio rules in a continuous-time model 1990Portfolio Selection with Transaction Costs 1986Capital Market Equilibrium with Transaction Costs 1992Numerical Methods for Stochastic Control Problems in Continuous Time 1991An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs 1989Optimization Problems in the Theory of Continuous Trading

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