Weakly Nonlinear Analysis of the Hamilton-Jacobi-Bellman Equation Arising from Pension Savings Management
Year: 2010
Author: Z. Macová, D. Ševčovič
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 4 : pp. 619–638
Abstract
The main purpose of this paper is to analyze solutions to a fully nonlinear parabolic equation arising from the problem of optimal portfolio construction. We show how the problem of optimal stock to bond proportion in the management of pension fund portfolio can be formulated in terms of the solution to the Hamilton-Jacobi-Bellman equation. We analyze the solution from qualitative as well as quantitative point of view. We construct useful bounds of solution yielding estimates for the optimal value of the stock to bond proportion in the portfolio. Furthermore, we construct asymptotic expansions of a solution in terms of a small model parameter. Finally, we perform sensitivity analysis of the optimal solution with respect to various model parameters and compare analytical results of this paper with the corresponding known results arising from time-discrete dynamic stochastic optimization model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-742
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 4 : pp. 619–638
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Hamilton-Jacobi-Bellman equation weakly nonlinear analysis asymptotic expansion fully nonlinear parabolic equation stochastic dynamic programming pension savings accumulation model.