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Optimal portfolios for DC pension plans under a CEV model. (English) Zbl 1162.91411
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 {\it P. Devolder, M. Bosch Princep} and {\it 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.

91B30Risk theory, insurance
91B28Finance etc. (MSC2000)
93E99Stochastic systems and stochastic control
Full Text: DOI
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