A population whose evolution is approximately described by a Laguerre diffusion process is considered. Let Y(t) be the number of individuals alive at time t and T(y, t{sub}0) be the first time Y(t) is equal to either 0 or d(> 0), given that Y(t{sub}0) = y is in (0, d). The aim is to minimize the expected value of a cost criterion in which the final cost is equal to 0 if Y(T) = d and to ∞ if Y(T) = 0. The case when the final cost is 0 (respectively ∞) if T is greater than or equal to (resp. less than) a fixed constant S is also solved explicitly. In both cases, the risk sensitivity of the optimizer is taken into account.
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