@Article{IJNAM-7-619,
author = {Macová , Z. and Ševčovič , D.},
title = {Weakly Nonlinear Analysis of the Hamilton-Jacobi-Bellman Equation Arising from Pension Savings Management},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2010},
volume = {7},
number = {4},
pages = {619--638},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/742.html}
}