TY - JOUR

T1 - Computation of optimal portfolios using simulation-based dimension reduction

AU - Boyle, Phelim

AU - Imai, Junichi

AU - Tan, Ken Seng

N1 - Funding Information:
The authors acknowledge the constructive comments of Raman Uppal and Marcel Rindisbacher and they thank Martina Wilhelm for research assistance. They are grateful to two anonymous referees for their constructive comments. Phelim Boyle acknowledges support from the Natural Sciences and Engineering Research Council of Canada. Junichi Imai is grateful for research supports from the Institute for Quantitative Finance and Insurance at the University of Waterloo and from Grant-in-Aid for Scientific Research in Japan Society for the Promotion of Science. Ken Seng Tan acknowledges funding from the Canada Research Chairs Program and the Natural Sciences and Engineering Research Council of Canada.

PY - 2008/12

Y1 - 2008/12

N2 - 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.

AB - 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.

KW - Asset allocation

KW - Dimension reduction

KW - Optimal portfolio selection

KW - Quasi-Monte Carlo

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U2 - 10.1016/j.insmatheco.2008.05.004

DO - 10.1016/j.insmatheco.2008.05.004

M3 - Article

AN - SCOPUS:56549121844

SN - 0167-6687

VL - 43

SP - 327

EP - 338

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 3

ER -