An insurance company sells a 1-yr policy that covers the loss of a home due to a catastrophic flood. the probability of a catastrophic flood loss for a policyholder during any year is 0.002. there is at most 1 loss per year. the maximum amt paid by the insurer is 300,000 per loss.

Given that a flood loss occurs, the amt of a catastrophic flood loss is uniformly distributed between 100,000 and 1,000,000.

What is the net premium for this policy?

I know that we have a uniform distribution, so calculated the mean and tried to multiply by the 0.002 somewhere but it is not seeming to work.

  • $\begingroup$ The question is vaguely ambiguous. "There is at most one loss per year" -- does that mean the policy only pays for one flood, or does it mean only one flood can happen? Also, from what you describe, you're not taking the deductible into account. I suggest you study the definitions and give this problem another try. $\endgroup$ – nomen Jun 9 '14 at 21:36
  • $\begingroup$ I did try the deductible approach, just a little lazy to describe everything here. It still didn't make sense $\endgroup$ – user156055 Jun 9 '14 at 21:43
  • $\begingroup$ You admit to being too lazy, so you want us to do it for you... $\endgroup$ – nomen Jun 9 '14 at 21:45

Let $F$ denote the event that a flood occurs. Let $(L|F)$ denote the loss due to a flood. Let $(B|F)$ denote the benefit paid given that a flood occurs. Since there is a deductible $d$, $(B|F) \sim \max\{0, (L|F) - d\}$.

Use the law of total expectation.

  • $\begingroup$ This still isn't clear. How do you use the probabilities and such? Can you provide a complete answer here? $\endgroup$ – user156055 Jun 9 '14 at 21:49
  • $\begingroup$ I would have, if you had put in even a tiny bit of demonstrable effort. We're volunteers here. We do this for fun. We're not here to do your homework for you. If this ample hint is not good enough, you are out of luck from me. $\endgroup$ – nomen Jun 10 '14 at 7:16

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