We discuss linear regression approaches to conditional Value-at-Risk and Average Value-at-Risk (Conditional Value-at-Risk, Expected Shortfall) risk measures. Two estimation procedures are considered for each conditional risk measure, one is direct and the other is based on residual analysis of...

This paper considers a class of functions referred to as convex-concave-convex (CCC) functions to calibrate unimodal or multimodal probability distributions. In discrete case, this class of functions can be expressed by a system of linear constraints and incorporated into an optimization...

A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called...

A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called...