SOA ERMEnterprise Risk Management (CERA / FSA cross-track)

Which copula exhibits zero upper-tail dependence regardless of its correlation parameter (for $|\rho|<1$)?

Annual losses are exponential with mean $\theta=1{,}000$. Calculate $TVaR_{0.95}$ using $VaR_p=-\theta\ln(1-p)$ and $TVaR_p=VaR_p+\theta$ for the exponential.

Explain why relying solely on linear (Pearson) correlation to model dependence between two lines of business can understate joint tail risk, and how a copula-based approach addresses this.