A potential customer for an $80,000 fire insurance policy possesses a home in an

Question

A potential customer for an $80,000 fire insurance policy possesses a home in an area that, according to experience, may sustain a total loss in a given year with probability of 0.001 and a 50% loss with probability 0.01. (a) Let Y = the payout on an individual policy. Ignoring all other partial losses, find the probability distribution for Y. (b) Let C be the premium that the insurance company charges. Write down the function giving the company's net gain/loss. What premium should the company charge for a yearly policy in order to break even on all $80,000 policies in this area?

Explanation / Answer

1. probability of a total loss in a given year is 0.001

and that of a 50% loss is 0.01

ingoring all other partial loss we have

probability of no loss is 1-0.001-0.01=0.989

a) Y=the payout on an individual policy

hence for total loss Y takes the value $80000

for 50% Y takes the value $80000*0.5=$40000

for no loss Y takes the value $0

hence the probability distribution of Y is

Y:               $80000          $40000          $0

P[Y=y]:      0.001            0.01             0.989

b) C be the premium that the insurance company charges

so the function giving the company's net gain/loss is

T=C-Y        if T>0 then that implies the gain and if T<0 then that implies the loss

hence the premium that the company should charge for a yearly policy in order to break even on all $80000 policies in the area is determined from

E[T]=0

or, E[C-Y]=0

or, C-E[Y]=0

now E[Y]=80000*0.001+40000*0.01+0*0.989=80+400=480

so C-480=0

or, C=$480

hence the required premium is $480 [answer]

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