tut03s - UNSW ACTL1001 Actuarial Studies and Commerce...

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Unformatted text preview: UNSW ACTL1001 Actuarial Studies and Commerce Sample Solutions Exercises 3 Exercise 1 For s ( x ) = q & 1 & x 100 for x < 100 we have 1. Pr [ a life aged 15 survives to 45 ] = s (45) s (15) = q & 1 & 45 100 q & 1 & 15 100 = r : 55 : 85 = 0 : 8044 2. 45 p 20 = s (65) s (20) = q & 1 & 65 100 q & 1 & 20 100 = r : 35 : 8 = 0 : 6614 1 3. Pr [ a life aged 20 will not survive to age 40 ] = 20 q 20 = 1 & 20 p 20 = 1 & s (40) s (20) = 1 & q & 1 & 40 100 q & 1 & 20 100 = 1 & r : 6 : 8 = 0 : 13397 4. Pr [ a life aged 20 will die between age 50 and 65 ] = 30 j 15 q 20 = s (50) & s (65) s (20) = q & 1 & 50 100 & q & 1 & 65 100 q & 1 & 20 100 = p : 5 & p : 35 p : 8 = 0 : 1291 5. q 40 = 1 & p 40 = 1 & s (41) s (40) = 1 & s 1 & 41 100 1 & 40 100 = 0 : 00837 Exercise 2 For s ( x ) = & 1 & x 100 3 for x < 100 we have 2 1. 10 p 20 = s (30) s (20) = & : 7 : 8 3 = 0 : 6699 2....
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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tut03s - UNSW ACTL1001 Actuarial Studies and Commerce...

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