Computation of optimal portfolios using simulation-based dimension reduction

This paper describes a simple and efficient method for determining the optimal portfolio for a risk averse investor. The portfolio selection problem is of long standing interest to finance scholars and it has obvious practical relevance. In a complete market the modern procedure for computing the optimal portfolio weights is known as the martingale approach. Recently, alternative implementations of the martingale approach based on Monte Carlo methods have been proposed. These methods use Monte Carlo simulation to compute stochastic integrals. This paper examines the efficient implementation of one of these methods due to [Cvitanic, J., Goukasian, L., Zapatero, F. 2003. Monte Carlo computation of optimal portfolios in complete markets. J. Econom. Dynam. Control 27, 971–986]. We explain why a naive application of the quasi-Monte Carlo method to this problem is often only marginally more efficient than the classical Monte Carlo method. Using the dimension reduction technique of [Imai, J., Tan, K.S., 2007. A general dimension reduction method for derivative pricing. J. Comput. Financ. 10 (2), 129–155] it is possible to significantly reduce the effective dimension of the problem. The paper shows why the proposed technique leads to a dramatic improvement in efficiency.