REFRACTION-REFLECTION STRATEGIES IN THE DUAL MODEL

摘要

We study the dual model with capital injection under the additional condition that the dividend strategy is absolutely continuous. We consider a refraction-reflection strategy that pays dividends at the maximal rate whenever the surplus is above a certain threshold, while capital is injected so that it stays non-negative. The resulting controlled surplus process becomes the spectrally positive version of the refracted-reflected process recently studied by Perez and Yamazaki (2015). We study various fluctuation identities of this process and prove the optimality of the refraction-reflection strategy. Numerical results on the optimal dividend problem are also given.