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**Optimal pension management in a stochastic framework.**
*(English)*
Zbl 1068.91028

Summary: We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund manager must cope with two background risks: the salary risk and the inflation risk. We find a closed form solution for the asset allocation problem and so we are able to analyze in detail the behavior of the optimal portfolio with respect to salary and inflation. Finally, a numerical simulation is presented.

### MSC:

91G10 | Portfolio theory |

90B15 | Stochastic network models in operations research |

93E20 | Optimal stochastic control |

### Keywords:

defined-contribution pension plan; salary risk; inflation risk; stochastic optimal control; Hamilton-Jacobi-Bellman equation
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\textit{P. Battocchio} and \textit{F. Menoncin}, Insur. Math. Econ. 34, No. 1, 79--95 (2004; Zbl 1068.91028)

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### References:

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