Survival maximization for a Laguerre population

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(0)(0)() be the first time Y(t) is equal to either 0 or d(> 0), given that Y(t)) = 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.