Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation
Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation
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DOI：
10.1007/s007800050075
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发表时间：
2000-06
影响因子：
1.7
通讯作者：
S. Asmussen;Bjarne Højgaard;M. Taksar
中科院分区：
文献类型：
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作者：
S. Asmussen;Bjarne Højgaard;M. Taksar
摘要：我们考虑了一个金融公司的模型，它必须找到一个平衡其风险和预期利润的最优策略。本文所举的例子涉及一家保险公司，其风险控制方法在业内被称为超额损失再保险。根据这一计划，保险公司将其部分保费流转移到另一家公司，以换取每笔超过一定水平的索赔的金额。这降低了风险，但也降低了潜在利润。目标是动态选择红利分配策略，使累积预期贴现红利支出最大化。我们使用扩散逼近来解决这个最优控制问题，其中考虑了两种情况：(A)红利支付率是无限制的，在这种情况下，这个问题在数学上变成了扩散过程的奇异-正则混合控制问题。它的分析部分涉及到一个线性二阶微分方程的自由边界(Stephan)问题。最优政策规定，使用一定的留存水平(取决于准备金)进行再保险，当准备金低于某个临界水平时，不支付股息，以支付超过的一切。再保险将在一个取决于索赔规模分布的水平停止。(B)红利支付率由某个正常数限定，在这种情况下，问题变成了一个常规的控制问题。在这里，最优政策是以一定的利率再保险，当准备金低于一定比率时不支付股息，当准备金超过准备金时以最高比率支付。在这种情况下，再保险可能会停止，也可能不会停止，这取决于索赔规模的分布和FM的规模，但在所有情况下，当准备金超过时，保留水平将保持不变。
Abstract.We consider a model of a financial corporation which has to find an optimal policy balancing its risk and expected profits. The example treated in this paper is related to an insurance company with the risk control method known in the industry as excess-of-loss reinsurance. Under this scheme the insurance company divert part of its premium stream to another company in exchange of an obligation to pick up that amount of each claim which exceeds a certain levela. This reduces the risk but it also reduces the potential profit. The objective is to make a dynamic choice ofaand find the dividend distribution policy, which maximizes the cumulative expected discounted dividend pay-outs. We use diffusion approximation for this optimal control problem, where two situations are considered:(a) The rate of dividend pay-out are unrestricted and in this case mathematically the problem becomes a mixed singular-regular control problem for diffusion processes. Its analytical part is related to a free boundary (Stephan) problem for a linear second order differential equation. The optimal policy prescribes to reinsure using a certain retention level (depending on the reserve) and pay no dividends when the reserve is below some critical leveland to pay out everything that exceeds. Reinsurance will stop at a leveldepending on the claim size distribution.(b) The rate of dividend pay-out is bounded by some positive constant, in which case the problem becomes a regular control problem. Here the optimal policy is to reinsure at a certain rate and pay no dividends when the reserve is belowand pay out at maximum rate when the reserve exceeds. In this case reinsurance may or may not stop depending on the claim size distribution and the size ofM, but in all cases the retention level will remain constant when the reserve exceeds.