Optimality of \((s, S)\) policies for jump inventory models (Q1935956)

In this paper the authors study the optimization of an inventory problem described by the differential equation \[ dx(t)=-(d+A(x(t))\chi_{(0,\infty)}(x(t)))-dN(t), \] where \(N\) is a Poisson process and \(A\) is a positive continuous function. The optimal control problem is given by the minimization of an infinite horizon cost under impulse control policies. They exhibit a so-called \((s,S)\) optimal policy. This paper extends some previous results by the same authors.