Value at Risk and Tail Value at Risk

Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) lesson in Severity, Frequency, and Aggregate Models. 13 min read, ~1,950 words.

VaR:, the -th quantile (the tail boundary). TVaR (continuous):, the average loss beyond the boundary. TVaR (discrete): via stop-loss. Exponential: and (memoryless, gap independent of ). Normal: and. Pareto:. TVaR VaR always; heavy tails widen the gap.