## Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time.(English)Zbl 1018.91028

The paper discusses the modelling and control of pension funds. A continuous-time stochastic pension fund model is proposed in which there are $$n$$ risky assets plus the risk-free asset as well as randomness in the level of benefit outgo. Markov control strategies optimize over the contribution rate and over the range of possible asset-allocation strategies. For general loss functions, it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. In the quadratic loss function case, an explicit solution for the optimal contribution and asset-allocation strategies is provided. The latter is found to be counterintuitive, hence power and exponential loss functions are then investigated.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 60H30 Applications of stochastic analysis (to PDEs, etc.)
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### References:

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