Quantitative methods for modelling and pricing dependenent insurance risks

想象一下，有一个20年期的年金池--每年支付共同生活水平的年金--发放给已婚夫妇。根据世界银行2008-2012年加拿大的数据，年金的未来寿命是根据加拿大2000-2002年、2a和2b的完整生命表，实际利率平均为0.7%。简单的计算表明，在寿命独立的标准假设下(而不是更现实的正相关性假设)，这些合同的价格明显被低估了。利差随着年龄的增长而增长，例如，一对65岁的男性和一名60岁的女性的典型夫妇的利差为12%。由于年金池中的随机支付本身是(相互)依赖的，减值变得相当令人生畏。更广泛地说，忽视风险投资组合内部和之间的相关性，可能而且经常确实会导致机构的偿付能力问题，甚至破产。**尽管如此，传统的精算模型仍然建立在独立的假设之上。尽管这是不现实的，但这种假设往往允许方便的简化，从而保证了理想的分析可操纵性。在拟议的研究中，我将背离这一假设。我将制定有意义的方法来描述保险风险之间的相关性，并研究这种相关性的含义。我将辩称，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部因素的依赖性。我将证明，刚才提到的定价规则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那么复杂的替代方案的绝对不利后果。

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.