Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR a...

By mid 2004, the Basel Committee on Banking Supervision (BCBS) is expected to launch its final recommendations on minimum capital requirements in the banking industry. Although there is the intention to arrive at capital charges which concur with economic intuition, the risk weight formulas proposed by the committee will lack an adequate treatment of concentration risks in credit portfolios. Th...

Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains such as finance. In this work we present a new formula for the gradient of the CVaR in the form of a conditional expectation. Our result is similar to policy gradients in the reinforcement learning literature. Based on this formula, we propose novel sampling-based estimators for the CV...

We consider continuous-time stochastic optimal control problems featuring Conditional Valueat-Risk (CVaR) in the objective. The major difficulty in these problems arises from timeinconsistency, which prevents us from directly using dynamic programming. To resolve this challenge, we convert to an equivalent bilevel optimization problem in which the inner optimization problem is standard stochast...

Recently, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several applications. For continuous distributions, CVaR is defined as the expected loss exceeding Value-at Risk (VaR). However, generally, CVaR is the weighted average of VaR and losses exceeding VaR. Central to the approach is an optimization technique for calculating VaR and optimizing...

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to ...

background: the incidence of ulcerative colitis (uc) is rising in populations with western-style diet, rich in fat and protein, and low in fruits and vegetables. in the present study, we aimed to evaluate the association between dietary protein intakes and the risk of developing incident uc.   methods : sixty two cases of uc and 124 controls were studied using country-specific food frequency qu...