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...

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 investigate the set of centers of completely and jointly mixable distributions. In addition to several results, we show that, for each n ≥ 2, there exist n standard Cauchy random variables adding up to a constant C if and only if |C| ≤ n*log(n − 1)/π

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...

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...

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing...

We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected...