Survival Maximization for a Laguerre Population

MARIO LEFEBVRE

《Mathematical Problems in Engineering》 2002卷 (2002/12) Pp. 563-574

https://doi.org/10.1080/1024123021000061944

摘要

A population whose evolution is approximately described by a Laguerre diffusion processis considered. Let Y(t) be the number of individuals alive at time t and T(y, t_0) be the first time Y(t) is equal to either 0 or d(＞ 0), given that Y(t_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.

關鍵字

Brownian motion ； Diffusion processes ； Stochastic control ； Risk sensitivity ； Hitting time ； Stochastic differential equation