Abstract

We study a stochastic control problem in which the underlying process follows a spectrally negative L´evy process. A controller can increase the process either continuously or at independent Poisson arrival times, each type of intervention incurring a different cost. We demonstrate the optimality of a hybrid barrier strategy, which increases the process continuously or at Poisson times whenever it falls below two respective lower barriers—one for continuous control and the other for Poisson control. The optimal strategy and the associated value function are expressed semi-explicitly using scale functions. Numerical results are also provided. This is a joint work with Jose Luis Perez (CIMAT) and Qingyuan Zhang (University of Queensland).