Abstract
This paper considers the combined optimal dividend, capital injection and reinsurance strategies for an insurance company. The proportion reinsurance is taken as a risk control, the variance principle is adopted by the insurer and the reinsurer with different parameter respectively. Furthermore, the insurer can control its surplus by paying dividends and injecting capitals, which incur both proportional and fixed costs. The value of the company is defined as the difference between the expected discounted dividends and the expected discounted capital injections until the time of bankruptcy. To maximize the value of the company, by solving the impulse problem, we obtain explicit solutions for value function and optimal strategy.
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