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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**Extra resources for Actuarial mathematics for life contingent risks**

**Example text**

00274 years. 2 × 10−5 . We can relate the force of mortality to the survival function from birth, S0 . 7) gives µx = = 1 S0 (x) − S0 (x + dx) lim S0 (x) dx→0+ dx 1 d − S0 (x) . S0 (x) dx Thus, µx = −1 d S0 (x). 9) From standard results in probability theory, we know that the probability density function for the random variable Tx , which we denote fx , is related to the distribution function Fx and the survival function Sx by fx (t) = d d Fx (t) = − Sx (t). 9) that µx = f0 (x) . S0 (x) We can also relate the force of mortality function at any age x + t, t > 0, to the lifetime distribution of Tx .

Regular Premium Deferred Annuity (RPDA) The RPDA offers a deferred life annuity with premiums paid through the deferred period. It is otherwise the same as the SPDA. Joint life annuity A joint life annuity is issued on two lives, typically a married couple. The annuity (which may be single premium or regular 12 Introduction to life insurance premium, immediate or deferred) continues while both lives survive, and ceases on the ﬁrst death of the couple. Last survivor annuity A last survivor annuity is similar to the joint life annuity, except that payment continues while at least one of the lives survives, and ceases on the second death of the couple.

2 × 10−5 . We can relate the force of mortality to the survival function from birth, S0 . 7) gives µx = = 1 S0 (x) − S0 (x + dx) lim S0 (x) dx→0+ dx 1 d − S0 (x) . S0 (x) dx Thus, µx = −1 d S0 (x). 9) From standard results in probability theory, we know that the probability density function for the random variable Tx , which we denote fx , is related to the distribution function Fx and the survival function Sx by fx (t) = d d Fx (t) = − Sx (t). 9) that µx = f0 (x) . S0 (x) We can also relate the force of mortality function at any age x + t, t > 0, to the lifetime distribution of Tx .

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

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