Survival maximization for a Laguerre population

Mathematical Problems in Engineering

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

DOI  :  

来源: DOAJ

【 摘 要 】

A population whose evolution is approximately described by a Laguerre diffusion process is considered. Let $Y\left(t\right)$be the number of individuals alive at time $t$ and $T\left(y,t_0\right)$ be the first time $Y\left(t\right)$ is equal to either $0$or $d\left(>0\right),$ given that $Y\left(t_0\right)=y$ is in $\left(0,d\right)$ The aim is to minimize the expected value of a cost criterion in which the final cost is equal to $0$ if $Y\left(T\right)=d$ and to $\infty$if $Y\left(T\right)=0.$ The case when the final cost is $0$ (respectively $\infty$) 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.

【 授权许可】

Unknown