Assignment 1 soln

Assignment 1 soln - FIN 3220A Actuarial Models I First Term...

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1 FIN 3220A Actuarial Models I First Term 2005-2006 Solutions to Assignment 1 1. The survival function is () 100 10 X x sx = for 0 x 100. Hence we have () () 75 75 100 75 1 75 1 75 1 , 10 2 11 75 , 100 20 100 75 1 100 1 75 . 75 1 2 50 XX x x X X Fs d fs x dx x f s = = =− = = = µ= = = 2. The calculations are as follows: ()() { } { } 22 50 2 50 2 50 50 9000 10 50 50 9000 10 51 51 50 51 6000 5889 111 , 50 6000 6000 9000 10 50 50 50 10 2 50 10 2 110 , 9000 50 6000 9000 10 50 50 1 . 6000 ss q s s x s q −− == = = + =⇒ µ = = = −µ = 3. The number of persons expected to survive to age 80 is 4 4 47 6 0 10 10 9 1000 1000exp ln 1000exp 4ln 1000 656.1. 99 1 0 pd t ⎧⎫ ⎛⎞ =−= = ⎨⎬ ⎜⎟ ⎝⎠ ⎩⎭ 4. The calculations are as follows: {} 1 1 2 2 00 0 0 12 2 1 0 1 1 ln ln 2 1 21 exp 1 . xt xx t dx t a x dt dt a x t ax t t x t + + +− + + ⎪⎪ = = + = −+ + µ = = ∫∫ 5. The calculations are as follows: 1 1 1 1 1. 1 1 2 1 sy m y ym my sy y m y + + ++ =⇒= + + Hence, the median future lifetime of ( y ) is 1 + y .
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2 6. From the given information, we have [] () 32 1 32 1 32 33 32 32 32 32 32 2 34 33 34 32 1 32 1 33 32 1 32 1 32 1 1 1 12 10 .
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This note was uploaded on 05/21/2011 for the course FIN 3220 taught by Professor Cswong during the Spring '05 term at CUHK.

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Assignment 1 soln - FIN 3220A Actuarial Models I First Term...

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