High performance computations for an optimal portfolio choice problem
A strategy for allocating wealth across time when agents face a set of stochastic investment opportunities is presented. This portfolio choice problem implies to solve numerically complex non-linear partial differential equations which requires powerful computer resources. The numerical method for solving this type of convection-diffusion equations in this framework is described. The algorithm is implemented on a vectorial computer and with a Single Program Multiple Data (SPMD) version on a dedicated Massively Parallel Processing (MPP) system. Efficiency of the method is evaluated on both architectures. Numerical results for real market conditions are presented using a wide range of parameter values to explore the validity domain of the algorithm.
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- 1.Brennan M., Schwartz E. and Lagnado R.: Strategic Asset Allocation. The John E. Anderson Graduate School of Management UCLA, working paper No 11–93, revised 1995.Google Scholar
- 2.Byrde O., Cobut D., Reymond J.-D. and Sawley M. L.: Parallel Multi-block Computation of Incompressible Flows for Industrial Applications. In: Proceedings of the Parallel Computational Fluid Dynamics (Pasadena, 1995) — Implementations and Results Using Parallel Computers, Elsevier 1996.Google Scholar
- 3.Cox J. and Huang C.: Optimum Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process. Journal of Economic Theory 49, pp. 33–83, 1989.Google Scholar
- 4.Ghashghaie S., Breymann W., Peinke J. and Talkner P.: Turbulence and Financial Markets. In: Gavrilakis S., Machiels L. and Monkewitz P.A. (eds), Proceedings of the Sixth European Turbulence Conference held in Lausanne, pp 167–170, July 1996.Google Scholar
- 5.Karatzas I., Lehoczky J., Sethi S. and Shreve S.: Explicit Solutions of a General Consumption/Investment Problem. Mathematics of Operation Research 11, pp. 261–94, 1986.Google Scholar
- 6.Merton R.: Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Journal of Economic Theory 3, pp. 373–413, 1971.Google Scholar
- 7.Merton R.: Continuous-Time Finance. Basil Blackwell, Cambridge, Massachusetts, 1990.Google Scholar
- 8.Reymond J.-D.: Accurate Grid Refinement for Complex Parallel Applications. In: Soni B. K., Eiseman P. R., Thompson J. F. and Häuser J. (eds), Numerical Grid Generation in Computational Fluid Dynamics and Related Fields (Proceedings of the 5th International Conference held at Mississippi State University, April 1996).Google Scholar
- 9.Sawley M. L., Byrde O., Reymond J.-D. and Cobut D. Parallel Computation of Incompressible Flow for Industrial Applications. In: Proceedings of the 12th Australian Fluid Mechanics Conference (Sydney, December 1995), Vol 2, pp 719–722.Google Scholar
- 10.Sethi S. and Taksar M.: Note on Merton's Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Journal of Economic Theory 46, pp. 395–401, 1988.Google Scholar
- 11.Wilmott P., Howison S. and Dewynne J.: The mathematics of financial derivatives. Cambridge University Press, Cambridge, 1995.Google Scholar