# Computation of optimal portfolios using simulation-based dimension reduction

Phelim Boyle, Junichi Imai, Ken Seng Tan

Research output: Contribution to journalArticle

5 Citations (Scopus)

### Abstract

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.

Original language English 327-338 12 Insurance: Mathematics and Economics 43 3 https://doi.org/10.1016/j.insmatheco.2008.05.004 Published - 2008 Dec

### Fingerprint

Optimal Portfolio
Dimension Reduction
Martingale
Monte Carlo method
Effective Dimension
Quasi-Monte Carlo Methods
Simulation
Portfolio Selection
Stochastic Integral
Reduction Method
Efficient Implementation
Finance
Pricing
Monte Carlo Simulation
Derivative
Computing
Alternatives
Dimension reduction
Optimal portfolio
Market

### Keywords

• Asset allocation
• Dimension reduction
• Optimal portfolio selection
• Quasi-Monte Carlo

### ASJC Scopus subject areas

• Statistics, Probability and Uncertainty
• Economics and Econometrics
• Statistics and Probability

### Cite this

Computation of optimal portfolios using simulation-based dimension reduction. / Boyle, Phelim; Imai, Junichi; Tan, Ken Seng.

In: Insurance: Mathematics and Economics, Vol. 43, No. 3, 12.2008, p. 327-338.

Research output: Contribution to journalArticle

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