Mathematical Problems in Engineering
Volume 8 (2002), Issue 6, Pages 563-574
doi:10.1080/1024123021000061944
Survival maximization for a Laguerre population
Département de mathématiques et de génie industriel, École Polytechnique de Montréal, C.P. 6079, Succursale Centre-ville, Montréal H3C 3A7, Québec, Canada
Received 10 December 2001
Copyright © 2002 Mario Lefebvre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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,t0) be the first time Y(t) is equal to either 0 or d(>0),
given that Y(t0)=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.