Optimal dividend and stopping problems for two-dimensional compound poisson risk model

Abstract

We consider a optimal dividend and stopping problem for two-dimensional compound Poisson risk model. The two companies allow to help each other by transffering payments. The goal of the companies is to maximize the expected cumulative discounted dividends payments up to the time of ruin. The problem is formulated as a singular control and optimal stopping problem. We explicitly construct the value function and the optimal strategy when claims are exponentially distributed and present two numerical examples.

Keywords:

• Two-dimensional compound Poisson risk model
• optimal dividend problem
• optimal stopping problem
• optimal strategy

Acknowledgments

The authors would like to express our sincere gratitude to an anonymous reviewers and the editors for their helpful comments and constructive suggestions, which help to improve the quality of the paper.

Additional information

Funding

This work was supported by National Natural Science Foundation of China under Grant [number 1207012113]; Science and Technology Project of Hebei Education Department [number QN2020273].