2. Consider exposure units subject to a binomial pure premium distribution. Assu

Question

2. Consider exposure units subject to a binomial pure premium distribution. Assume that the amount of each loss is S500, that an insurance company has insured 200 such units during the past year, and that 20 losses have occured. The company plans to insure 250 exposure units during the coming year, and it is evident that the probability of loss will increase by 50% and the severity by 10 percent from this year to the next. Interpret this information and comment on which numerical information can be retrieved from them in aspects of a risk manager.

Explanation / Answer

In the previous year each loss amount is given to be equal to $500, and there were 20 losses out of the 200 units insured. Therefore the probability of a loss given here is 20/200 = 0.1.

Now we are given here that each of the loss will increase by 50% in the next year therefore it would be 500*1.5 = 750 in the next year. Also the probability of a loss is to increase by 10%. Therefore it would be become 0.1*1.1 = 0.11

This basically helps the risk manager to analyze the situation in terms of expected loss from the 250 exposure units in the next year.

The expected number of losses in the next year would be given as:

= np = 250*0.11 = 27.5 that is approx 28 losses are expected in the next year.

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