## Survival maximization for a Laguerre population.(English)Zbl 1043.92024

The paper considers a certain one-dimensional diffusion process which is a generalization of the Laguerre process and is used in genetics to model the evolution of a certain population. The problems of forcing this diffusion process to take on the value $$d>0$$ before $$0,$$ and that of forcing the process to remain above $$0$$ for at least a fixed time $$s,$$ are studied in this paper. The aim of both problems is to maximize the survival time of the population. The risk sensitivity of the optimizer is taken into account in both problems.

### MSC:

 92D15 Problems related to evolution 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 93E20 Optimal stochastic control 60J60 Diffusion processes
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