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.


91G10 Portfolio theory
90B15 Stochastic network models in operations research
93E20 Optimal stochastic control
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[4] Boulier, J.-F.; Huang, S.-J.; Taillard, G., Optimal management under stochastic interest, Insurance: Mathematics and Economics, 28, 173-189 (2001) · Zbl 0976.91034
[6] Cox, J. C.; Ingersoll, J.; Ross, S., A theory of the term structure of interest rates, Econometrica, 53, 385-408 (1985) · Zbl 1274.91447
[7] Cox, J. C.; Huang, C. F., A variational problem arising in financial economics, Journal of Mathematical Economics, 20, 465-487 (1991) · Zbl 0734.90009
[8] Deelstra, G.; Grasselli, M.; Koehl, P.-F., Optimal investment strategies in the presence of a minimum guarantee, Insurance: Mathematics and Economics, 33, 189-207 (2003) · Zbl 1074.91013
[10] El Karoui, N.; Jeanblanc-Picqué, M., Optimization of consumption with labor income, Finance and Stochastics, 2, 409-440 (1998) · Zbl 0930.60050
[12] Haberman, S.; Vigna, E., Optimal investment strategy for defined contribution pension schemes, Insurance: Mathematics and Economics, 28, 233-262 (2001) · Zbl 0976.91039
[14] Lioui, A.; Poncet, P., On optimal portfolio choice under stochastic interest rates, Journal of Economic Dynamic and Control, 25, 1841-1865 (2001) · Zbl 0979.91032
[15] Menoncin, F., Optimal portfolio and background risk: an exact and an approximated solution, Insurance: Mathematics and Economics, 31, 249-265 (2002) · Zbl 1055.91054
[16] Merton, R. C., Lifetime portfolio selection under uncertainty: the continuous-time case, Review of Economics and Statistics, 51, 247-257 (1969)
[17] Merton, R. C., Optimum consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502
[21] Vasiček, O. E., An equilibrium characterisation of the term structure, Journal of Financial Economics, 5, 177-188 (1977) · Zbl 1372.91113
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