Actuarial mathematics for life contingent risks by D C M Dickson; Mary Hardy; H R Waters

By D C M Dickson; Mary Hardy; H R Waters

Balancing rigour and instinct, and emphasizing purposes, this contemporary textual content is perfect for college classes and actuarial examination preparation.

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2 The future lifetime random variable 19 which can be written as S0 (x + t) = S0 (x) Sx (t). 4) This is a very important result. It shows that we can interpret the probability of survival from age x to age x + t as the product of (1) the probability of survival to age x from birth, and (2) the probability, having survived to age x, of further surviving to age x + t. 1) is equal to Pr[Tx > t]. Similarly, any survival probability for (x), for, say, t + u years can be split into the probability of surviving the first t years, and then, given survival to age x + t, subsequently surviving another u years.

2 Explain why an insurer might demand more rigorous evidence of a prospective policyholder’s health status for a term insurance than for a whole life insurance. 3 Explain why premiums are payable in advance, so that the first premium is due now rather than in one year’s time. 4 Lenders offering mortgages to home owners may require the borrower to purchase life insurance to cover the outstanding loan on the death of the borrower, even though the mortgaged property is the loan collateral. (a) Explain why the lender might require term insurance in this circumstance.

3, we noted the importance of the force of mortality. A further significant point is that when mortality data are analysed, the force of mortality 36 Survival models is a natural quantity to estimate, whereas the lifetime distribution is not. The analysis of mortality data is a huge topic and is beyond the scope of this book. An excellent summary article on this topic is Macdonald (1996). For more general distributions, the quantity f0 (x)/S0 (x), which actuaries call the force of mortality at age x, is known as the hazard rate in survival analysis and the failure rate in reliability theory.

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