IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas
The Clayton copula has the form C(u,v) = (u^(-a) + v^(-a) - 1)^(-1/a) with a > 0. For a = 1, what is C(0.5, 0.5)?
C(0.5,0.5) equals 1/3, about 0.3333. Substituting a = 1 gives 2 + 2 - 1 = 3, and the inverse is 1/3. This exceeds the independence value of 0.25, which is consistent with positive dependence in the Clayton copula.
- A0.25
- B0.3333Correct
- C0.5
- D0.4
- 0.1667
Explanation
With a = 1: u^(-1) + v^(-1) - 1 = 2 + 2 - 1 = 3. So C = 3^(-1) = 0.3333. Check: it lies between the independence value 0.25 and the upper bound 0.5, as expected for positive dependence. 0.25 is wrong because it is the independence copula value.
Did you get it right without looking?
One question tells you little. A timed set on Introduction to copulas shows your real accuracy, how long you take and where you lose marks.
More Introduction to copulas questions
- Which statement about tail dependence in common copulas is correct?
- A Gumbel copula C(u,v) = exp(-[(-ln u)^θ + (-ln v)^θ]^(1/θ)) with θ = 2 is used for two Indian insurer's catastrophe losses. The upper tail …
- A Gaussian copula with correlation parameter 0.6 is used to link two loss variables. Which statement about its tail dependence is correct?
- Sklar's theorem states that for a joint distribution function F with marginals F1 and F2, there exists a copula C such that:
- Two Indian insurers' annual claim totals X and Y have continuous marginals. Their copula is C(u,v)=uv. Which statement is correct about P(X …
- If X has a continuous distribution function F_X, which statement is used to obtain the uniform inputs for a copula from observed losses?