A two-dimensional dividend problem for collaborating companies and an optimal stopping problem

We consider two insurance companies with wealth processes described by two independent Brownian motions with drift. The goal of the companies is to maximize their expected aggregated discounted dividend payments until ruin. The companies are allowed to help each other by means of transfer payments....

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Bibliographic Details
Published in:Scandinavian actuarial journal 2019-01, Vol.2019 (1), p.80-96
Main Author: Grandits, Peter
Format: Article
Language:English
Subjects:
Actuarial science
Dividend optimization
Economic models
free boundary
optimal control problem
optimal stopping problem
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Summary:We consider two insurance companies with wealth processes described by two independent Brownian motions with drift. The goal of the companies is to maximize their expected aggregated discounted dividend payments until ruin. The companies are allowed to help each other by means of transfer payments. But in contrast to Gu et al. [(2018). Optimal dividend strategies of two collaborating businesses in the diffusion approximation model. Mathematics of Operations Research 43(2), 377-398], they are not obliged to do so, if one company faces ruin. We show that the problem is equivalent to a mixture of a one-dimensional singular control problem and an optimal stopping problem. The value function is explicitly constructed and a verification result is proved. Moreover, the optimal strategy is provided as well.
ISSN:0346-1238
1651-2030
DOI:10.1080/03461238.2018.1498387