Optimal Dividend Strategies of Two Collaborating Businesses in the Diffusion Approximation Model

In this paper, we consider the optimal dividend payment strategy for an insurance company that has two collaborating business lines. The surpluses of the business lines are modeled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs, while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occurs.