Quantitative methods for modelling and pricing dependenent insurance risks

想象一下，一个20年期的共同生活水平年金池，每年支付，到期发给已婚夫妇。年金的未来寿命是根据加拿大完整生命表2000 - 2002，2a和2b，根据世界银行2008 - 2012年加拿大数据，真实的利率平均为0.7%。简单的计算表明，在寿命独立的标准假设下（与更现实的强正相关假设相反），合同的价格被大大低估。这种差距随着年龄的增长而增长，例如，对于一对65岁的男子和一名60岁的女子的典型夫妇来说，差距为12%。由于池中年金的随机付款本身（相互）依赖，减值变得相当令人生畏。更一般地说，忽视风险组合内部和之间的依赖关系可能而且经常导致偿付能力问题，甚至导致机构破产。** 尽管如此，传统的精算模式是基于独立性的假设。虽然不切实际，但这种假设通常允许方便的简化，从而保证了理想的分析易处理性。在本研究中，我将偏离这一假设。我将制定有意义的方式来描述保险风险之间的依赖关系，并研究这种依赖关系的影响。我认为，为保险风险定价的规则必须考虑到它们对伴随风险以及其他外生因素的依赖性。我将证明，刚刚提到的定价规则并不一定会导致难以忍受的棘手问题，值得一试，特别是考虑到它们不太复杂的替代品的完全不利后果。

Imagine a pool of 20-year term annually-paid joint life level annuities-due issued to married couples. The future lifetimes of the annuitants are per Complete Life Tables Canada 2000 - 2002, 2a and 2b, and the real interest rate is an average of .7%, as per World Bank's 2008 - 2012 Canadian data. Simple calculations show that under the standard assumption of independence of lifetimes (as opposed to a more realistic one of strong positive dependence), the contracts are significantly underpriced. The spreads grow with age and are, for instance, 12% for a typical couple of a 65 old man and a woman aged 60. As the random payments due to the annuities in the pool, are themselves (inter)dependent, the impairment becomes rather daunting. More generally, neglecting dependencies within and among portfolios of risks can and often does lead to solvency issues and even bankruptcy of institutions. **Notwithstanding, traditional actuarial models rest on the assumption of independence. Unrealistic as it is, the assumption often allows for convenient simplifications and thus guarantees a desirable level of analytic tractability. In the proposed research, I will depart from this assumption. I will formulate meaningful ways to describe dependencies amongst insurance risks and study the implications of such dependencies. I will argue that the rules assigning prices to insurance risks must take into consideration their dependencies on companion risks, as well as on other exogenous factors. I will demonstrate that the just-mentioned pricing rules do not necessarily lead to unbearable intractabilities and are worthy a try, in particular given the utterly adverse consequences of their less sophisticated alternatives.