A life company sells a term to a 21-year-old male that pays 0,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of 0 each year as payment for the . The amount X that the company earns on this policy is 0 per year, less the 0,000 that it must pay if the insured dies. Here is the distribution of X. Fill in the missing probability in the table and calculate the mean profit X.

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Age at death 21 22 23 24 25 26

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Profit -,750 -,500 -,250 -,000 -,750 50
Probability 0.00185 0.00189 0.00191 0.00194 0.00198 ?

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? =
Mean profit = $

Thank u!

 

  • Nick S 1:05 pm on March 28, 2010

    I’ll get you started.

    In the first year, the company receives the $250 premium (at the beginning of the year, BTW) and one of two things happens: either the insured dies (prob 0.00185) or doesn’t (prob 0.99815). If he dies, the company pays $100K. So the profit in the first year is
    $250 – 0.00185x$100K = $250 – $185 = $65.

    In the second year, again the company receives $250 and the insured dies or doesn’t. The profit in the second year is
    $250 – 0.00189x$100K = $250 – $189 = $61. And so on.

    BUT if the insured doesn’t survive the year, he doesn’t go on to the next year–he stops paying the premium.

    So when you calculate the mean profit, you have to reduce it in the later years by the probability that the insured has already died.

    For example, the profit contribution in the second year is really only $61 x 0.99815.

  • Jiang F 1:05 pm on March 28, 2010

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