Optimality of Refraction Strategies for Spectrally Negative Levy Processes

Daniel Hernandez-Hernandez, Jose-Luis Perez, Kazutoshi Yamazaki

Published 2015-04-14Version 1

We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Levy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs of the running and controlling costs. Under the assumption that the running cost function is convex, we show the optimality of a refraction strategy. The proof of convergence to the reflection strategy as well as numerical illustrations are also given.