Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model.

*(English)*Zbl 1231.91402Summary: This paper focuses on the constant elasticity of variance (CEV) model for studying the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using Legendre transform, dual theory and variable change technique, we derive the explicit solutions for the power and exponential utility functions in two different periods (before and after retirement). Each solution contains a modified factor which reflects an investor’s decision to hedge the volatility risk. In order to investigate the influence of the modified factor on the optimal strategy, we analyze the property of the modified factor. The results show that the dynamic behavior of the modified factor for the power utility mainly depends on the time and the investor’s risk aversion coefficient, whereas it only depends on the time in the exponential case.

##### MSC:

91G10 | Portfolio theory |

91G80 | Financial applications of other theories |

93E20 | Optimal stochastic control |

##### Keywords:

annuity; defined contribution pension plan; stochastic optimal control; Legendre transform; CEV model
Full Text:
DOI

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