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Unformatted text preview: UNSW ACTL1001 Actuarial Studies and Commerce Tutorial Solutions 1 Exercise 1 Say the company sells n policies. In this case from the solution to Exercise 1.4 in Chapter 1 of the text we have that if the premium charged is P then the number of claims that will ruin the company will be determined by the first claim that makes claim payments greater than premium income plus capital so that the breakeven number of claims is i = n × P + 40 , 000 100 , 000 Now the company requires a probability of ruin of 0.05 so that we need to determine i so that the probability of i or more claims is (less than) 0.05. The probability of j claims out of the n policies is n j (0 . 01) j (0 . 99) n- j so we require n X j = i n j (0 . 01) j (0 . 99) n- j ≤ . 05 In Excel we can evaluate this probability as 1-BINOMDIST(j-1,n,0.01,true) since BINOMDIST ( j,n, . 01 , “ true ”) = j X i =0 n i (0 . 01) i (0 . 99) n- i For n = 100 we have the probability of the different number of claims from Excel We see that...
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- Three '11
- Probability theory, Summation