Optimality of an $(s,S)$ Policy with Compound Poisson and Diffusion Demands: A Quasi-Variational Inequalities Approach

This paper revisits the paper of Bensoussan, Liu, and Sethi where they proposed a single item continuous-time inventory model where demand is a mixture of a diffusion process and a compound Poisson process. They showed that in a continuous review setting an (s, S) policy is optimal when the jump sizes are exponentially distributed. However, the case where the jump sizes are general was not solved completely. This paper solves this case. [PUBLICATION ABSTRACT]