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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
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