IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas
For a bivariate copula C, the upper tail dependence coefficient is defined as the limit, as u approaches 1 from below, of a conditional probability. Which expression gives it?
The upper tail dependence coefficient is the limit as u tends to 1 of P(U1 > u | U2 > u). It measures the chance that one variable is extreme in the upper tail given that the other is, so it captures joint extreme large losses.
- Alim P(U1 > u | U2 > u)Correct
- Blim P(U1 < u | U2 < u)
- Clim P(U1 > u | U2 < u)
- Dlim P(U1 < u | U2 > u)
- lim of C(u,u) as u tends to 1
Explanation
Upper tail dependence measures the probability that one uniform variable is extremely large given that the other is extremely large. So it is the limit of P(U1 > u | U2 > u) as u tends to 1. The lower-tail version uses P(U1 < u | U2 < u) as u tends to 0, so that option is the wrong tail.
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