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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 info for Actuarial mathematics for life contingent risks
Reversionary annuity A reversionary annuity is contingent on two lives, usually a couple. One is designated as the annuitant, and one the insured. No annuity beneﬁt is paid while the insured life survives. On the death of the insured life, if the annuitant is still alive, the annuitant receives an annuity for the remainder of his or her life. 4 Other insurance contracts The insurance and annuity contracts described above are all contingent on death or survival. There are other life contingent risks, in particular involving shortterm or long-term disability.
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. Regular premiums may be paid annually, semi-annually, quarterly, monthly or weekly. Monthly premiums are common as it is convenient for policyholders to have their outgoings payable with approximately the same frequency as their income.
6. 1. 1 Kx and ex In many insurance applications we are interested not only in the future lifetime of an individual, but also in what is known as the individual’s curtate future lifetime. The curtate future lifetime random variable is deﬁned as the integer part of future lifetime, and is denoted by Kx for a life aged x. If we let denote the ﬂoor function, we have Kx = Tx . We can think of the curtate future lifetime as the number of whole years lived in the future by an individual. As an illustration of the importance of curtate future lifetime, consider the situation where a life aged x at time 0 is entitled to payments of 1 at times 1, 2, 3, .