Quantitative methods for modelling and pricing dependenent insurance risks

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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.