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Life Insurance

The insurance industry recently experienced a high demand for life insurance policies issued to married couples, with payoff due at the second spouse s death. The fair pricing of such policies is an example of insurance problems requiring the construction of two or higher dimensional survival functions.

Unfortunately, while a lot of information is available regarding univariate survival functions, little data can be found allowing for estimation of the association between them.

The assumption of independent univariate survival functions of the spouses is not supported by empirical data. The parametric copula models currently used for bivariate constructions are based on spouses physical age only. They do not explicitly address such factors as "common disaster"and "broken heart", related to real (chronological) time.

We suggest a modification of existing copula models using Bayesian approach, which allows us to incorporate existing information concerning univariate survival functions. Numerical results are presented for MLE and Bayesian estimation. A direction for further research is suggested.

INVESTMENT GUARANTEES

In the United Kingdom, unit-linked insurance rose in popularity in the late 1960s through to the late 1970s, typically combining a guaranteed minimum payment on death or maturity with a mutual fund type investment. These contracts also spread to areas such as Australia and South Africa, where U.K. insurance companies were in uential. In the United States, variable annuities and equity-indexed annuities offer different forms of equity-linking guarantees. In Canada, segregated fund contracts became popular in the late 1990s, often incorporating complex guaranteed values on death or maturity.

Germany recently introduced equity-linked endowment insurance. Similar contracts are also popular in many other jurisdictions. In this book the term is used to refer to any contract that incorporates guarantees dependent on the performance of a stock market indicator. We also use the term to refer to the group of products that includes variable annuities, segregated funds, and unit-linked insurance. For each of these products, some or all of the premium is invested in an equity fund that resembles a mutual fund. That fund is the separate account and forms the major part of the bene t to the policyholder. Separate account products are the source of some of the most important risk management challenges in modern insurance, and most of the examples in this book come from this class of insurance. The nature of the risk to the insurer tends to be low frequency in that the stock performance must be extremely poor for the investment guarantee to bite, and high severity in that, if the guarantee does bite, the potential liability is very large.

The assessment and management of nancial risk is a very different proposition to the management of insurance risk. The management of insurance risk relies heavily on diversi cation. With many thousands of policies in force on lives that are largely independent, it is clear from the central limit theorem that there will be very little uncertainty about the total claims. Traditional actuarial techniques for pricing and reserving utilize deterministic methodology because the uncertainties involved are relatively minor. Deterministic techniques use best estimate values for interest rates, claim amounts, and (usually) claim numbers. Some allowance for uncertainty and random variation may be made implicitly, through an adjustment to the best estimate values. For example, we may use an interest rate that is 100 or 200 basis points less than the true best estimate. Using this rate will place a higher value on the liabilities than will using the best estimate as we assume lower investment income.

Investment guarantees require a different approach. There is generally only limited diversi cation amongst each cohort of policies. When a market indicator becomes unfavorable, it affects many policies at the same time. For the simplest contracts, either all policies in the cohort will generate claims or none will. We can no longer apply the central limit theorem. This kind of risk is referred to as systematic, systemic, nondiversi able This kind of risk is referred to as or risk.