6 papers
Dirichlet sub-mixtures: A new reading of multiplicative background risk models with Pareto margins
Nawaf Mohammed, Edward Furman
Multiplicative background risk models (MBRMs) provide a tractable framework for describing dependent risks. We construct a class of MBRMs with Pareto margins by combining Marshall-…
A tale of two allocations: Risk capital contributions versus risk contributions in the tail
Nawaf Mohammed, Edward Furman
We compare two natural proportional notions of a risk component's contribution to the aggregate tail risk of a collection of risks: the fraction of aggregate tail risk capital allo…
The Elliptically Optimal Confidence Interval: A Bivariate Extension of Wilson's Score Method
Nawaf Mohammed
Constructing a confidence interval for the difference between two independent binomial proportions involves a nuisance direction that is not identified by the estimand. The one-sam…
Joint Exclusivity
Nawaf Mohammed
We introduce joint exclusivity (JE), a relaxation of mutual exclusivity (ME) for non-negative random vectors that forbids only the simultaneous positivity of all components. Wh…
When Is the Gini Loading More Prudent? Tail Structure and the Ordering of the Standard Deviation and the Gini Mean Difference
Nawaf Mohammed
The standard deviation (SD) and the Gini mean difference (GMD) are the two canonical measures of variability used to load premiums, set risk margins and allocate capital, yet no un…
VaR at Its Extremes: Impossibilities and Conditions for One-Sided Random Variables
Nawaf Mohammed
Value-at-Risk (VaR) may reward diversification at some probability levels and penalize it at others. We study the two extremal regimes in which one effect prevails at every level s…