Key Words: systemic risk, conditional value at risk, CoVaR, marginal expected shortfall, MES, systemically important financial institutions, SIFIs
(2) In this paper, we focus on two of these proposed measures: conditional value at risk (CoVaR) and marginal expected shortfall (MES).
We include the conditional value at risk ([xi] + 1/1 - [alpha] [[SIGMA].sup.w.sub.w=1] [[pi].sub.w] [[eta].sub.w]) and the parameter P to represent the risk aversion level.
Equation (9) provides the constraint associated to the calculation of conditional value at risk. Equation (10) shows the nature of the decision variables in the model and Equation (11) expresses the binary variable indicating whether a contract c is chosen on stage w.
The conditional value at risk
(CVaR) is a risk measure, defined as the expected loss conditional on the benefit payment ratio being higher than a given value at risk (VaR).
* r'v > [sub.SSD]r'w if and only if [CVaR.sub.[alpha]](-r'v) [less than or equal to] CVaR[alpha](-r'w) for all [alpha] [member of] <0,1> where conditional value at risk
(CVaR) of portfolio w can be defined via optimization problem:
We define conditional Value at Risk
as conditional expected loss under the condition that it exceeds Value at Risk:
Manganelli, "CA ViaR: Conditional Value at Risk
by Quantile Regression," NBER Working Paper No.
In the supply chain risk ordering decision problem, many people adopt a risk approach, that is, establishing the ordering model of supply chain based on conditional value at risk
(CVaR) (2000) .