an:05563947
Zbl 1162.91411
Gao, Jianwei
Optimal portfolios for DC pension plans under a CEV model
EN
Insur. Math. Econ. 44, No. 3, 479-490 (2009).
00250041
2009
j
91B30 91B28 93E99
defined contribution pension plan; stochastic optimal control; CEV model; HJB equation; optimal portfolios
Summary: This paper studies the portfolio optimization problem for an investor who seeks to maximize the expected utility of the terminal wealth in a DC pension plan. We focus on a constant elasticity of variance (CEV) model to describe the stock price dynamics, which is an extension of geometric Brownian motion. By applying stochastic optimal control, power transform and variable change technique, we derive the explicit solutions for the CRRA and CARA utility functions, respectively. Each solution consists of a moving Merton strategy and a correction factor. The moving Merton strategy is similar to the result of \textit{P. Devolder, M. Bosch Princep} and \textit{I. Dominguez Fabian} [Insur. Math. Econ. 33, No. 2, 227--238 (2003; Zbl 1103.91346)], whereas it has an updated instantaneous volatility at the current time. The correction factor denotes a supplement term to hedge the volatility risk. In order to have a better understanding of the impact of the correction factor on the optimal strategy, we analyze the property of the correction factor. Finally, we present a numerical simulation to illustrate the properties and sensitivities of the correction factor and the optimal strategy.
Zbl 1103.91346