By D C M Dickson; Mary Hardy; H R Waters
Balancing rigour and instinct, and emphasizing purposes, this contemporary textual content is perfect for collage classes and actuarial examination preparation.
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Extra resources for Actuarial mathematics for life contingent risks
5 years, (x) must ﬁrst survive 10 years. 5), for all ages greater than x. For all the distributions used in this book, we make three additional assumptions: Assumption 1. Sx (t) is differentiable for all t > 0. Note that together with d Condition 3 above, this means that dt Sx (t) ≤ 0 for all t > 0. Assumption 2. limt→∞ t Sx (t) = 0. Assumption 3. limt→∞ t 2 Sx (t) = 0. These last two assumptions ensure that the mean and variance of the distribution of Tx exist. These are not particularly restrictive constraints – we do not need to worry about distributions with inﬁnite mean or variance in the context of individuals’ future lifetimes.
Single Premium Immediate Annuity (SPIA) This contract is the same as the SPDA, except that the annuity commences as soon as the contract is effected. This might, for example, be used to convert a lump sum retirement beneﬁt into a life annuity to supplement a pension. As with the SPDA, there may be a guarantee period applying in the event of the early death of the annuitant. Regular Premium Deferred Annuity (RPDA) The RPDA offers a deferred life annuity with premiums paid through the deferred period.
6 Premiums A life insurance policy may involve a single premium, payable at the outset of the contract, or a regular series of premiums payable provided the policyholder survives, perhaps with a ﬁxed end date. In traditional contracts the regular premium is generally a level amount throughout the term of the contract; in more modern contracts the premium might be variable, at the policyholder’s discretion for investment products such as equity-linked insurance, or at the insurer’s discretion for certain types of term insurance.