IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory
Fire claims from a Mumbai portfolio exceed a threshold of ₹10 lakh. Exceedances are modelled by a Generalised Pareto distribution with ξ = 0.25 and β = ₹5 lakh. What is the expected excess over the threshold, E[X − u | X > u]?
The mean excess of a Generalised Pareto distribution at the threshold is β/(1 − ξ). With β = ₹5 lakh and ξ = 0.25 this is 5/0.75 = ₹6.67 lakh. Options using β(1+ξ) or β(1−ξ) misapply the formula.
- A₹5.00 lakh
- B₹6.25 lakh
- C₹20.00 lakh
- D₹3.75 lakh
- ₹6.67 lakhCorrect
Explanation
For a GPD with ξ < 1, the mean excess is β/(1 − ξ) = 5/0.75 = 6.67 lakh. Option ₹6.25 lakh wrongly uses β(1+ξ). Option ₹3.75 lakh uses β(1−ξ). Option ₹5 lakh ignores ξ.
Did you get it right without looking?
One question tells you little. A timed set on Introduction to extreme value theory shows your real accuracy, how long you take and where you lose marks.
More Introduction to extreme value theory questions
- A GEV distribution has location mu = 50, scale sigma = 10 and shape xi = -0.5. Its distribution function is F(x) = exp(-[1 + xi(x-mu)/sigma]…
- Losses are independent and uniformly distributed on (0, 1) (in Rs crore). For a block of n = 5 losses, what is the expected value of the blo…
- Block maxima of a loss variable are fitted with a generalised extreme value distribution with shape parameter ξ. For which value of ξ is the…
- Which statement about the Fisher–Tippett–Gnedenko theorem is correct?
- A GEV distribution has shape parameter ξ = 0.4. Which statement about the tail of this distribution is correct?
- Block maxima of daily losses are modelled by a GEV distribution with shape ξ > 0 after suitable normalisation. Which statement is correct?