## Optimal contributions in a defined benefit pension scheme with stochastic new entrants.(English)Zbl 1117.91380

Summary: This paper focuses on the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme. Classical results in the actuarial literature on pension plan population theory have been extended to the stochastic case. The paper formulates the trade-off between risk and cost of contribution strategies. Then, using a constrained nonlinear programming approach, optimal contributions strategies have been derived and the trade-off solved by means of identifying an efficient frontier. Finally, a numerical application has been carried out, showing the inefficiency of certain classical normal cost methods.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 91D20 Mathematical geography and demography

### Keywords:

Optimal normal cost
Full Text:

### References:

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