On a stochastic demand jump inventory model

This paper considers a Quasi-Variational Inequality (QVI) arising from a stochastic demand jump inventory model in a continuous review setting with a fixed ordering cost and where demand is made up of a deterministic part (which is a function of the stock level) punctuated by random jumps. Under some restrictions on the parameters, a solution to the QVI is found which corresponds to an (s,S)(s,S) policy.