L4-Slide-232-2010W

L4-Slide-232-2010W - Lecture 4, January 14 1.6 Life Table...

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Lecture 4, January 14 1.6 Life Table Consider a group of l 0 newborn lives and assume that their lives are independent with the same s.f. S 0 ( x ) . (a) Denote the number of survivors at age x ( 0) from the group by L x and let l x denote the expected number of survivors at age x from the group or l x = E ( L x ) . Note that L x has a binomial df b ( l 0 ,S 0 ( x )) . Then l x = l 0 S 0 ( x ) = l 0 x p 0 , x 0 , or equivalently , S 0 ( x ) = l x l 0 , x 0 . 1
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Other actuarial functions can be expressed in terms of l x : μ x = - S 0 0 ( x ) S 0 ( x ) = - l 0 x l x , x 0 , f 0 ( x ) = S 0 ( x ) μ x = - l 0 x l 0 , x 0 , t p x = S 0 ( x + t ) S 0 ( x ) = l x + t l x , t 0 . 2
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x and x + n from the group by n D x and let Let n d x denote the expected number of deaths between ages x and x + n or n d x = E ( n D x ) . Note that n D x = L x - L x + n . Then, n d x = l x - l x + n = d x + ··· + d x + n - 1 = Z n 0 l x + s μ x + s ds. n
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This note was uploaded on 03/20/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Summer '08 term at Waterloo.

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L4-Slide-232-2010W - Lecture 4, January 14 1.6 Life Table...

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