For a distribution of losses you are given: x Pr(X <= x) E(X min x) 50 0.40 40 75 0.50 50 100 0.60 65 150 0.80 82 200 0.90 95 infinity 1.00 110 An insurance policy reimburses a loss subject to a deductible of 50. The deductible is then raised so that only two-thirds of the number of losses that exceeded the old deductible will exceed the new deductible. Determine the percent change in the expected value of the claim payment per payment random variable when the deductible is raised. (Ans Decrease of 3.57%)
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40 Pr(X <= x + 50) = 0.80 E(X min x) = 0.50 E(X max x) = 100 Therefore, the expected value of the claim payment is $40.50. Show more…
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Losses (prior to any deductibles being applied) have a distribution as reflected in the table below. x F(x) E(X | x) 10,000 0.6 6000 15,000 0.7 7700 22,500 0.8 9500 32,500 0.9 11000 ∞ 1.0 20000 There is a per-loss ordinary deductible of 10,000. The deductible is then raised so that half the number of losses exceed the new deductible as exceeded the old deductible. Determine the percentage change in the expected claim per payment when the deductible is raised.
Sri K.
Insured Loss An insurance policy is written to cover a loss, $X$ where $X$ has a uniform distribution on $[0,1000] .$ At what level must a deductible be set in order for the expected payment to be 25$\%$ of what it would be with no deductible? Choose one of the following. (Hint: Use a variable, such as $D,$ for the deductible. The payment is 0 if the loss is less than $D,$ and the loss minus $D$ if the loss is greater than $D .$ Source: Society of Actuaries. $$ \begin{array}{llll}{\text { a. } 250} & {\text { b. } 375} & {\text { c. } 500} & {\text { d. } 625} & {\text { e. } 750}\end{array} $$
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Losses After Deductible A manufacturer's annual losses follow a distribution with density function $$ f(x)=\left\{\begin{array}{ll} \frac{2.5(0.6)^{2.5}}{x^{3.5}} & \text { for } x>0.6 \\ 0 & \text { otherwise. } \end{array}\right. $$ To cover its losses, the manufacturer purchases an insurance policy with an annual deductible of $2 .$ What is the mean of the manufacturer's annual losses not paid by the insurance policy? Choose one of the following. (Hint: The loss not paid by the insurance policy will equal the actual loss if the actual loss is less than the deductible. Otherwise it will equal the deductible.) Source: Society of Actuaries. a. 0.84 b. 0.88 c. 0.93 d. 0.95 e. 1.00
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