HW_PS1_Key_S08

HW_PS1_Key_S08 - PAM 423 Problem Set 1 Solutions Spring...

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PAM 423 Problem Set 1 - Solutions Spring 2008 Q1.) (a) This new loss distribution was derived by subtracting the $1,000 deductible from each of the loss amounts. Since Tanni is responsible for paying the first $1,000 of any loss, the insurance company is now concerned only about losses greater than $1,000. (b) 2300 $ ) ( ) 0.1($10000 0.2($5000) 0.3($1000) 0.4($0) ) ( ) ( 1 = + + + = = = x E x E x p x E N i i i 86 . 3163 ) ( ) ( ) ( 10010000 Var(x) 2300) - 0.1(10000 2300) - 0.2(5000 2300) - 0.3(1000 2300) - 0.4(0 ) ( )) ( ( ) ( 2 2 2 2 2 1 = = = + + + = - = = x SD x Var x SD x Var x E x p x Var i N i i (c) 1700 $ ) ( 0.1($9000) 0.2($4000) 0.7($0) ) ( ) ( 1 = + + = = = x E x E x p x E N i i i 2900 ) ( ) ( ) ( 8410000 Var(x) 1700) - 0.1(9000 1700) - 0.2(4000 1700) - 0.7(0 ) ( )) ( ( ) ( 2 2 2 2 1 = = = + + = - = = x SD x Var x SD x Var x E x p x Var i N i i (d) Tanni should be charged a lower premium for the second policy since both the expected value and variance of her loss are less under this plan. The amount the insurance company expects to pay out for a loss is less under the deductible plan, and this savings would be passed on to the consumer. The distribution under the deductible plan is also less variable, meaning the insurance company can be more certain of Tanni’s loss. However, with independent losses and large numbers of exposures the variability is less 1
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important to the insurance company than the expected value. Pooling the independent losses of many individuals allows an insurer to be fairly certain of their total losses, despite individual variability. In practice, insurance company’s also charge less for
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This note was uploaded on 05/19/2008 for the course PAM 4230 taught by Professor Tennyson during the Spring '07 term at Cornell.

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HW_PS1_Key_S08 - PAM 423 Problem Set 1 Solutions Spring...

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