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# Lecture%209 - Life Insurance and Superannuation Models Week...

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Life Insurance and Superannuation Models Week 9: Multiple Decrement Models April 27, 2011 1 / 22

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Week 9: Multiple State Transition Models Summary of Lecture Multiple decrement tables Several causes of decrement Probabilities of decrement Forces of decrement The Associated Single Decrement Tables Constructing the MDT from the associated SDT Uniform distribution of decrement References CT5 Chapters 13 and Bowers, et al. Chapter 10 ACTL3002: Week 9 2
Examples of Multiple Decrement Models Multiple decrement models are extensions of standard mortality models whereby there is simultaneous operation of several causes of decrement. A life fails because of one of the decrements. Examples include: Life insurance contract is terminated because of death/survival or withdrawal (lapse). An insurance contract provides coverage for disability and death, which are considered distinct claims. Life insurance contract pays a different benefit for different causes of death (e.g. accidental death benefits are doubled). Pension plan provides benefit for death, disability, employment termination and retirement. ACTL3002: Week 9 3

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Introducing Notation age number of employees deaths withdrawals overseas transfers x ( al ) x ( ad ) d x ( ad ) w x ( ad ) ot x 20 100,000 452 5,517 2,569 21 91,462 433 4,780 2,431 22 83,818 414 4,136 2,302 23 76,966 402 4,076 2,264 ACTL3002: Week 9 4
Introducing Notation cont... Conventional notation: ( al ) x represents the surviving population present at exact age x . ( ad ) k x represents the number of lives exiting from the population between ages x and x + 1 due to decrement k . It is also conventional to denote the total number of exits by all modes between ages x and x + 1 by ( ad ) x , i.e. ( ad ) x = m summationdisplay k = 1 ( ad ) k x where m is the total number of possible decrements, and therefore, ( ad ) x = ( al ) x - ( al ) x + 1 . ACTL3002: Week 9 5

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Probabilities of Decrement The probability that life ( x ) will leave the group within one year as a result of decrement k : ( aq ) k x = ( ad ) k x / ( al ) x . The probability that life ( x ) will leave the group (regardless of decrement): ( aq ) x = ( ad ) x / ( al ) x = m summationdisplay k = 1 ( ad ) k x / ( al ) x = m summationdisplay k = 1 ( aq ) k x .
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Lecture%209 - Life Insurance and Superannuation Models Week...

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