By D C M Dickson; Mary Hardy; H R Waters
ISBN-10: 0511632436
ISBN-13: 9780511632433
ISBN-10: 0511633637
ISBN-13: 9780511633638
ISBN-10: 0511651694
ISBN-13: 9780511651694
ISBN-10: 0521118255
ISBN-13: 9780521118255
Balancing rigour and instinct, and emphasizing purposes, this contemporary textual content is perfect for college classes and actuarial examination preparation.
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10 Introduction to life insurance because of an impairment, or a dangerous occupation, leaving around 2–3% who will be refused insurance. The rigour of the underwriting process will depend on the type of insurance being purchased, on the sum insured and on the distribution process of the insurance company. Term insurance is generally more strictly underwritten than whole life insurance, as the risk taken by the insurer is greater. Under whole life insurance, the payment of the sum insured is certain, the uncertainty is in the timing.
6 It is common for insurers to design whole life contracts with premiums payable only up to age 80. Why? 7 Andrew is retired. He has no pension, but has capital of $500 000. He is considering the following options for using the money: (a) Purchase an annuity from an insurance company that will pay a level amount for the rest of his life. (b) Purchase an annuity from an insurance company that will pay an amount that increases with the cost of living for the rest of his life. (c) Purchase a 20-year annuity certain.
18) that fx (t) = t px µx+t = − d t px . 21) From the definition of an expected value, we have ∞ ◦ ex = t fx (t)dt 0 ∞ = t t px µx+t dt. 21) to evaluate this integral using integration by parts as ∞ ◦ ex = − d t px dt dt t 0 = − t t px ∞ 0 ∞ − t px dt . 2 we stated the assumption that limt→∞ t t px = 0, which gives ∞ ◦ ex = t px dt. 22) 30 Survival models Similarly, for E[Tx2 ], we have ∞ E[Tx2 ] = t 2 t px µx+t dt 0 ∞ =− d t px dt dt t2 0 = − t 2 t px ∞ 0 ∞ − t px 2t dt 0 ∞ =2 t t px dt. 23) 0 So we have integral expressions for E[Tx ] and E[Tx2 ].
Actuarial mathematics for life contingent risks by D C M Dickson; Mary Hardy; H R Waters
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