In this paper, we investigate the asymptotic behavior of the portfolio diversification ratio based on Value-at-Risk (quantile) under dependence uncertainty, which we refer to as "worst-case diversification limit." We show that the worst-case diversification limit is equal to the upper limit of...

We propose a theory for rating financial securities based on a concept of self-consistency, which does not allow issuers to gain, by tranching financial securities, from investors who rely on the rating criterion. While the expected loss criterion used by Moody's satisfies self-consistency, the...

Research related to aggregation, robustness, and model uncertainty of regulatory risk measures, for instance, Value-at-Risk (VaR) and Expected Shortfall (ES), is of fundamental importance within quantitative risk management. In risk aggregation, marginal risks and their dependence structure are...

Many optimization problems in probabilistic combinatorics and mass transportation impose fixed marginal constraints. A natural and open question in this field is to determine all possible distributions of the sum of random variables with given marginal distributions; the notion of joint...

Following the results of Rüschendorf and Uckelmann (2002) [20], we introduce the completely mixable distributions on and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem for convex functions f...

We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. An END sequence has a partial sum which, subtracted by its mean, does not diverge as the number of random variables goes to infinity. We show that an END...

This paper investigates macroprudential policies and their role in containing systemic risk in China. It shows that China faces systemic risk in both the time (procyclicality) and cross-sectional (contagion) dimensions. The former is reflected as credit and asset price risks, while the latter is...