The Basel Committee on Banking Supervision (BCBS) (2013) recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The BCBS (2013) noted that - a number of weaknesses have been identified with using VaR for determining regulatory capital...

The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some...

A spectrum of upper bounds (Qα(X ; p) ae[0,∞] on the (largest) (1-p)-quantile Q(X;p) of an arbitrary random variable X is introduced and shown to be stable and monotonic in α, p, and X , with Q0(X ;p) = Q(X;p). If p is small enough and the distribution of X is regular enough, then Qα(X ; p)...