Optimal proportional reinsurance and dividend payments with transaction costs and internal competition

We study the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside company and transaction costs when dividends occur. The management of the company controls the reinsurance rate, the timing and the amount of dividends paid out to maximize the expected total dividends paid out to the shareholders until ruin time. By solving the corresponding quasi-variational inequality, we obtain the optimal return function and the optimal strategy.