## Optimality of an $$(s,S)$$ policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach.(English)Zbl 1194.93215

Summary: 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.

### MSC:

 93E20 Optimal stochastic control 49J40 Variational inequalities 65C30 Numerical solutions to stochastic differential and integral equations 90B05 Inventory, storage, reservoirs 49N25 Impulsive optimal control problems
Full Text: