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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory

Fire losses for a portfolio are modelled as independent with a common exponential distribution with mean Rs 2 lakh. In a block of 3 claims, what is the probability that the largest claim is at most Rs 2 lakh?

The probability is (1 - e^-1) cubed, about 0.2526. One claim falls below its mean with probability 0.6321, and all three independent claims must do so for the maximum to be at most Rs 2 lakh.

  1. A(1 - e^-1)^3 ≈ 0.2526Correct
  2. B1 - e^-3 ≈ 0.9502
  3. C3(1 - e^-1) ≈ 1.896
  4. D(1 - e^-3)^3 ≈ 0.8580
  5. e^-3 ≈ 0.0498

Explanation

F(2 lakh) = 1 - e^-1 = 0.6321. P(max <= 2 lakh) = F^3 = 0.6321^3 = 0.2526. Using e^-3 or 1 - e^-3 wrongly treats the event as a single claim exceeding a threshold of 3 means.

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