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

Annual losses are normal with mean 50 and standard deviation 20. Using $z_{0.995}=2.576$, calculate economic capital defined as $VaR_{99.5\%}$ minus expected loss.

Two risk modules each require stand-alone capital of 100. Their correlation is 0.5. Calculate the diversification benefit from aggregating them with the square-root formula.

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

Distinguish risk appetite, risk tolerance and risk limits, and give an example of each for a mid-sized commercial casualty insurer.

Describe the three sections of a U.S. NAIC ORSA Summary Report and explain how a reserving actuary's work feeds each.

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.

A firm's total diversified economic capital is 300, and TVaR-based contributions of two business units are 180 and 120 (already summing to the total under Euler allocation). Calculate business unit 1's allocated capital as a percentage of the total.

List the components typically found in a well-constructed risk appetite statement and explain why each is necessary for the statement to be operational rather than aspirational.

Distinguish hedging from diversification as risk-mitigation strategies, and give one example of each for a life insurer with a large fixed-annuity block exposed to interest-rate risk.

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.