Introduction to the Theory of Probabilistic Functions and Percentiles (Value-at-Risk)

摘要: Probabilistic and quantile (percentile) functions are commonly used for the analysis of models with uncertainties or variabilities in parameters. In financial applications, percentile losses is called Value-at-Risk (VaR). VaR, a widely performance measure, answers question: what maximum loss specified confidence level? Percentiles also defining other relevant measures, such as Conditional (CVaR). CVaR (also Mean Excess Loss, Shortfall, Tail VaR) average worst x% scenarios (e.g., 5%). risk measure has more attractive properties compared to VaR. This introductory paper gives basic definitions reviews several topics: sensitivities probabilistic functions; sensitivities percentiles (VaR); optimization approaches CVaR.