Exact tail asymptotics of aggregated parametrised risk

Exact Tail Asymptotics of Dirichlet Distributions

Abstract: Let X be a generalised symmetrised Dirichlet random vector inIR, k ≥ 2, and let tn ∈IRk, n ≥ 1 be such that limn→∞ P {X > tn} = 0. In this paper we derive an exact asymptotic expansion of P {X > tn} as n → ∞, assuming that the associated random radius of X has distribution function in the Gumbel max-domain of attraction.

Beta-gamma tail asymptotics

We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of Bubeck, Mossel, and Rácz in order to determine the tail asymptotics of the maximum degree of the preferential attachment tree. The proof presented here is s...

Hard edge tail asymptotics

Let Λ be the limiting smallest eigenvalue in the general (β, a)-Laguerre ensemble of random matrix theory. That is, Λ is the n ↑ ∞ distributional limit of the (scaled) minimal point drawn from the density proportional to ∏ 1≤i 0, a > −1; for β = 1, 2, 4 and integer a, this object governs the singular values of certain rank n Ga...

Asymptotics for risk capital allocations based on Conditional Tail Expectation

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodo...

Exact Asymptotics of Minimax Bahadur Risk in Lipschitz Regression