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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 nonnegative. The resulting controlled surplus process becomes the spectrally positive version of the refracted-reflected process recently studied by Pérez and Yamazaki [20]. 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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This page is a summary of: REFRACTION–REFLECTION STRATEGIES IN THE DUAL MODEL, Astin Bulletin, October 2016, Cambridge University Press,
DOI: 10.1017/asb.2016.28.
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