Optimal risk control and dividend distribution policies for a diffusion model with terminal value ☆
- Jingfeng Xu Ming Zhou .
- China Institute for Actuarial Science, Central University of Finance and Economics, 39 South College Road, Haidian, Beijing 100081, China
Received 16 April 2011. Revised 23 December 2011. Accepted 23 December 2011. Available online 9 January 2012.
In this paper we investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then the objective is set to make a dynamic choice of reinsurance policy and dividend distribution policy, which maximizes the sum of the expected discounted dividends up to ruin time and the expected discounted terminal value.
There are two novelties in this paper. Firstly, we formulate
the optimal control problem in terms of general reinsurance control policies. Each of the proportional reinsurance, the excess-of-loss reinsurance and combination of the two can be treated as a special case. It is shown that, under an expected premium principle, the dynamic excess-of-loss reinsurance is of optimal type within the general reinsurance contracts. Secondly, considering the excess-of-loss reinsurance policy and terminal value, we obtain the explicit expressions for the value function and optimal control policies by solving the HJB equation method. At the end of this paper numerical calculations are done to illustrate the influence of the terminal value on the value function and optimal policies as well.
- Cheap reinsurance Dividend Excess-of-loss reinsurance Expected value principle HJB equation Terminal value
Supported by a research grant of Chinese social science of State Education Ministry (10YJC790310 ) and a research grant of China Institute for Actuarial Science at University of Finance and Economics .Source: www.sciencedirect.com