Computation of optimal portfolios using simulation-based dimension reduction
AbstractThis 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 43 (2008)
Issue (Month): 3 (December)
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Web page: http://www.elsevier.com/locate/inca/505554
Optimal portfolio selection Asset allocation Dimension reduction Quasi-Monte Carlo;
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- Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
- Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan Storud, 2004.
"A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability,"
NBER Working Papers
10934, National Bureau of Economic Research, Inc.
- Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
- Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000.
"A Monte-Carlo Method for Optimal Portfolios,"
CIRANO Working Papers
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
- Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
- Fredrik Åkesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.
- Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
- Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
- Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
- Canner, Niko & Mankiw, N Gregory & Weil, David N, 1997.
"An Asset Allocation Puzzle,"
American Economic Review,
American Economic Association, vol. 87(1), pages 181-91, March.
- Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March.
- S. Ninomiya & S. Tezuka, 1996. "Toward real-time pricing of complex financial derivatives," Applied Mathematical Finance, Taylor and Francis Journals, vol. 3(1), pages 1-20.
- Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
- Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
- Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
- Lioui, Abraham, 2007. "The asset allocation puzzle is still a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1185-1216, April.
- Isabelle Bajeux-Besnainou & James V. Jordan & Roland Portait, 2001. "An Asset Allocation Puzzle: Comment," American Economic Review, American Economic Association, vol. 91(4), pages 1170-1179, September.
- Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
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