# 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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Additional resources for Actuarial mathematics for life contingent risks

Example text

Consider, for example, a whole life insurance contract issued to a life aged 50. The sum insured may not be paid for 30 years or more. The premiums paid over the period will be invested by the insurer to earn signiﬁcant interest; the accumulated premiums must be sufﬁcient to pay the beneﬁts, on average. 9 Exercises 15 to be incurred in maintaining the policy. The actuary may take into consideration the probability that the policyholder decides to terminate the contract early. The actuary may also consider the proﬁtability requirements for the contract.

Nevertheless, the Gompertz model does provide a fairly good ﬁt to mortality data over some age ranges, particularly from middle age to early old age. 07, for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs. 4 For x = 20, the force of mortality is µ20+t = Bc20+t and the survival function is −B 20 t c (c − 1) . 10): µ20+t = f20 (t) −B 20 t ⇒ f20 (t) = µ20+t S20 (t) = Bc20+t exp c (c − 1) . 2 shows the corresponding probability density functions. These ﬁgures illustrate some general points about lifetime distributions.

Then, when all of these factors have been modelled, they must be combined to set a premium. Each year or so, the actuary must determine how much money the insurer or pension plan should hold to ensure that future liabilities will be covered with adequately high probability. This is called the valuation process. For with-proﬁt insurance, the actuary must determine a suitable level of bonus. The problems are rather more complex if the insurance also covers morbidity risk, or involves several lives.