It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other one in a given sample (which hap...
In this paper we investigate portfolio optimization in a Black-Scholes continuoustime setting under quantile based risk measures: value at risk, capital at risk and relative value...
Value-at-Risk (VaR) is one of the most widely accepted risk measures in the financial and insurance industries, yet efficient optimization of VaR remains a very difficult problem....
The portfolio optimization problem is modeled as a mean-risk bicriteria optimization problem where the expected return is maximized and some (scalar) risk measure is minimized. In ...
General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such...
R. Tyrrell Rockafellar, Stan Uryasev, Michael Zaba...