Use the information in Figure 4.2 pertaining to a loss of $50,000 that occurs ra

Question

Use the information in Figure 4.2 pertaining to a loss of $50,000 that occurs randomly with a probability of one in one hundred. If the insurance company charges $750 per person per year, what is the load above the actuarially fair premium? If one hundred people are in the group, will the insurance company show an underwriting profit? Will the insurance company ever break even? How likely is it that the plan will show a loss next year? With 50 people in the group, is it more or less likely that the plan will show a loss? What about with 500 people? How large does the group have to be before the insurance company can be 99 percent sure that it will show an underwriting gain for the year?

FIGURE 4.2 Variability Declines as the Size of the Risk-Sharing Pool Increases $2,000 $1,500 99% Confidence Limit $1,000 Expected average loss $500- $500 S0 200 500 1,000 2,000 5,000 10,000 20,000 Number of People in Risk Pool

Explanation / Answer

The loss ammount is given as $50,000 that can occur randomly with a probability of 1/100=0.01

Therefore the Actuarily Fair Premium=Loss Ammount*(Probaility of the loss)

  =$50,000*(0.01)

=$500

Now,the copmany pays an actual premium of $750 per person per year basis.

Hence,the load fee in this case=Actual Premium paid by company-Actuarilly Fair Premium

  =$750-$500

=$250

From the figure 4.2,which basically illustrates the probability distribution of the expected loss of the insurance company with an average or mean expected loss of $500 within 99% confidence interval.Now,observe that based on 99% confidence interval,as the number of people in the risk sharing pool decreases both the probability of underwriting profit and loss for the company statistically increases.Hence,it can be stated with 99% statistical confidence that when the number of people in the risk sharing pool is 100,observe that there is indeed a likelihood of attaining underwriting profit by the company as the under 99% confidence interval the expected loss does have a likelihood of becoming less than zero when the number of people in sharing pool is 100 corresponding to the figure.

Furthermore,the 99% confidence interval further implies that there is a likelihood with 99% confidence that the company can attain the break even point when the number of people in the risk sharing pool are actually less than or equal to 750 or 800 approximately again corresponding to fugure 4.2.

With 50 people in the risk sharing group the likelihood of expected loss statistically increases with 99% confidence level as notice that the confidence interval expands as number of people in the risk pool decreases further.Now,observe that with 500 people there is still likelihood of underwriting profit for company with 99% confidence and the likelihood of expected loss decreases compared to only 50 people in the group as the interval contracts with more number of people in the group.Hence,compared to 50 people,the likelihood of expected loss is statistically lesser with 500 people in the group under the 99% confidence interval.

Estimation from the figure indicates that if number of people in the risk sharing pool increases in next year then the likelihood of expected loss will statistically decreases based on the 99% confidence interval.

As shown in the figure, risk group has to consist of a maximum of approximately 750 or 800 people for the copmany to have any likelihood of underwriting gain or profit for the year with 99% confidence or surity.

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