This paper examines the asymptotic risk of nested least-squares averaging estimators when the averaging weights are … selected to minimize a penalized least-squares criterion. We find conditions under which the asymptotic risk of the averaging …

A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications … for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of … on the website. The case study was done with the Portfolio Safeguard (PSG) optimization package, which has precoded risk …