An insurance company has the following claim payments to mak

An insurance company has the following claim payments to make:

time (years) payment
          1       $1,000
          2      $2,000

And the following bonds to choose from:

            Yrs to maturity Annual coupon Par value          Price
                  1                     4%            $1,000 $1,000.00
                    2                     5%            $1,000    $1,000.00
                    2                     0%            $1,000 $   915.73

What is the cost to the company, to nearest penny, to match the claim payments exactly?

Note: provide two answers.

Solution

the company has a 2% chance of having to pay you $2,000, or, another way to look at this is the company expects to lose on average 0.02($2,000) = $40 by insuring your computer. Similarly, the expected loss on insuring your iPhone is 0.03($400) = $12. To estimate, on average, what it would cost the company to insure all four items, we compute the following sum: The $90 represents, on average, what the company can expect to pay out on a policy such as yours. b) The $90 in part a) is telling us that if the insurance company were to write one million policies like this, it would expect to pay 1,000,000 × ($90) = $90,000,000 in claims. If the company is to make a profit, it must charge more than $90 as a premium, so it seems like a $100 premium is reasonable. ] The amount of $90 we found in Example 1 is called the expected value of the claims paid by the insurance company. We will now give the formal definition of this notion

0.02($2,000) + 0.03($400) +0.01($600) +0.04($800)= $90.