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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
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