保险投资组合中可预见和不可预见风险的定价
Pricing foreseeable and unforeseeable risks in insurance portfolios
摘要：
在这篇文章中，我们提出了一种定价保险产品的方法，不仅包括传统的风险，但也不可预见的。通过考虑泊松过程参数是一个混合的随机变量，我们捕获的异质性的可预见和不可预见的风险。为了说明这一点，我们估计了葡萄牙保险公司真实数据集的两个风险流的权重。为了计算保险费，我们将频率和严重程度设置为属于线性指数族的分布。贝叶斯设置下，我们表明，当工作与共轭先验的有限混合，保费可以估计的混合后验均值，更新参数，根据索赔历史。我们通过选择重尾分布来强调不可预见趋势的风险。在使用期望最大化算法估计了分布参数后，我们发现贝叶斯保费比传统保费对索赔趋势更具反应性。
英文摘要：
In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity of foreseeable and unforeseeable risks. To illustrate, we estimate the weights for the two risk streams for a real dataset from a Portuguese insurer. To calculate the premium, we set the frequency and severity as distributions that belong to the linear exponential family. Under a Bayesian setup , we show that when working with a finite mixture of conjugate priors, the premium can be estimated by a mixture of posterior means, with updated parameters, depending on claim histories. We emphasise the riskiness of the unforeseeable trend, by choosing heavy-tailed distributions. After estimating distribution parameters involved using the Expectation-Maximization algorithm, we found that Bayesian premiums derived are more reactive to claim trends than traditional ones.
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