论文标题
在平均变化溢价原理下的最佳再保险，以最大程度地减少毁灭的可能性
Optimal Reinsurance under the Mean-Variance Premium Principle to Minimize the Probability of Ruin
论文作者
论文摘要
我们考虑通过购买以平均值的溢价原则计算的再保险来最大程度地减少毁灭概率的问题，该保费是预期价值和差异溢价原则的结合。我们得出了最佳再保险策略的封闭形式表达式，以及在经典的cramér-lundberg风险过程的扩散近似下，毁灭的最小概率受到扩散的影响。我们找到了重新保险策略的明确表达，该表达式最大化了通过扩散扰动的经典风险过程的调整系数。同样，对于这个风险过程，我们使用随机Perron的方法来证明毁灭的最小概率是其汉密尔顿 - 雅各比 - 贝尔曼方程的独特粘度解决方案，并具有适当的边界条件。最后，我们证明，在经典风险过程的适当缩放下，毁灭的最小概率会收敛到扩散近似下毁灭的最小概率。
We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We derive closed-form expressions of the optimal reinsurance strategy and the corresponding minimum probability of ruin under the diffusion approximation of the classical Cramér-Lundberg risk process perturbed by a diffusion. We find an explicit expression for the reinsurance strategy that maximizes the adjustment coefficient for the classical risk process perturbed by a diffusion. Also, for this risk process, we use stochastic Perron's method to prove that the minimum probability of ruin is the unique viscosity solution of its Hamilton-Jacobi-Bellman equation with appropriate boundary conditions. Finally, we prove that, under an appropriate scaling of the classical risk process, the minimum probability of ruin converges to the minimum probability of ruin under the diffusion approximation.
