Abstract This paper focuses on a class of variational inequalities (VIs), where the map defining VI is given by component-wise conditional value-at-risk (CVaR) random function. We focus solving using sample average approximation, solutions are estimated with that uses empirical estimates CVaRs. establish two properties for this scheme. First, under continuity and uncertainty taking values in bo...

Abstract Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail while adapting to evolving market information. In this paper, we propose an approach constructing simultaneous confidence bands (SCBs) for as measured by CVaR CES, with the uniformly valid a set of levels. We consider one-sided (downside or upside...

Abstract: In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall the notion of conditional, dynamic and time-consistent risk measures. We link the latter with its iterated pr...

Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector necessitating that each component satisfy a marginal domain of attraction condition. Heffernan and Tawn (2004) and Heffernan and Resnick (2007) developed an approximation to the joint distribution of the random vector by conditioning that one of the components be extre...

Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariat...

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We model conditional market beta and alpha as flexible functions of state variables identified via a formal variable selection procedure. In the post-1963 sample, beta of the value premium comoves strongly with unemployment, inflation, and price-earnings ratio in a countercyclical manner. We also uncover a novel nonlinear dependence of alpha on business conditions: It falls sharply and becomes ...