In this paper, we characterize explicitly the first derivative of the Value at Risk and the Expected Shortfall with respect to portfolio allocation when netting between positions exists. As a particular case, we examine a simple Gaussian example in order to illustrate the impact of netting...

We define several concepts of dependence between default risk and recovery risk, in a factor model framework. These concepts are illustrated and compared from the perspective of structural models: Merton (1974)'s single horizon and single firm model, multi-factor extensions, possibly under a...

We develop a new method for generating dynamics of conditional correlation matrices between asset returns. These correlation matrices will be parameterized by a subset of their partial correlations,whose structure will be described by an undirected graph called 'vine.' Since such partial...

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systemic factors and random recoveries. As a significant improvement with respect to the literature, we detail all...

We consider a nonparametric method to estimate copulas, i.e. functions linking joint distributions to their univariate margins. We derive the asymptotic properties of kernel estimators of copulas and their derivatives in the context of a multivariate stationary process satisfactory strong mixing...

We define a new approach to manage prepayment, default and interest rate risks simultaneously in some standard asset-backed securities structures. We propose a parsimonious top-down approach, by modeling directly the portfolio loss process and the amortization process. Both are correlated to...

The central question of this paper is how to enhance supervised learning algorithms with fairness requirement ensuring that any sensitive input does not "`unfairly"' influence the outcome of the learning algorithm. To attain this objective we proceed by three steps. First after introducing...