An optimal stopping problem for jump diffusion logistic population model (Q1793351)

Summary: This paper examines an optimal stopping problem for the stochastic (Wiener-Poisson) jump diffusion logistic population model. We present an explicit solution to an optimal stopping problem of the stochastic (Wiener-Poisson) jump diffusion logistic population model by applying the smooth pasting technique [\textit{S. Dayanik} and \textit{I. Karatzas}, Stochastic Processes Appl. 107, No. 2, 173--212 (2003; Zbl 1075.60524); \textit{A. Dixit}, I moti Browniani e l'arte dell' incollare (Italian). Milano: Giuffrè Editore (1997; Zbl 0997.60508)]. We formulate this as an optimal stopping problem of maximizing the expected reward. We express the critical state of the optimal stopping region and the optimal value function explicitly.