Refraction-reflection strategies in the dual model

2015/11/24 by Pérez, José-Luis, Yamazaki, Kazutoshi
#60G51 #91B30 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.07918

Abstract

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 positive. The resulting controlled surplus process becomes the spectrally positive version of the refracted-reflected process recently studied by Pérez 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.

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