Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation

Asymptotics for ultimate ruin probability in a by-claim risk model

“…It provides an integrated framework for modelling extreme risks (claims) with both heavy tails and asymptotic (in)dependence. Recent works in this direction include [3,7,17,18], among others.…”

Asymptotics for VaR and CTE of total aggregate losses in a bivariate operational risk cell model

“…Finally, we turn to Theorem 3.3, for which the settings for N 1 (t) and N 2 (t) are the same as those in Theorem 3.1 with parameters θ N and ρ N for the Frank and Gumbel copulas, respectively; the generic severity random vector (X (1) , X (2) ) is modelled via the Gumbel copula of the form (17) with parameter ρ X ≥ 1, and has a common distribution F ∈ R −α for some α > 0. Then, by Lemma 5.2 of [35], (X (1) , X (2) ) ∈ BRV −α (F ) for some reference distribution F , and it can be calculated that for any Borel set…”

“…The concept of multivariate regular variation (MRV) is a natural extension of univariate regular variation, which provides an integrated framework for modelling extreme losses with both heavy tails and asymptotic (in)dependence in finance, insurance and risk management after the pioneer work from [17]. More related works on MRV include [24], [3], [35], [34], [33] among many others. We briefly introduce a special case of MRV with two dimensions.…”

A limit distribution of credit portfolio losses with low default probabilities

“…Credit risk management, although long residing in the finance literature, has attracted much research attention in the insurance/actuarial community; some recent papers include Vandendorpe et al (2008), Donnelly and Embrechts (2010), Tang and Yuan (2013), Bernardi et macroeconomic variables are important factors that affect the recovery rate, although none is consistently statistically significant. The determinants found in the literature can serve as guidance for latent variable specification in our model, although we do not purport, also it is not possible, that the latent variable can summarize all important default determinants; see also Duffie et al (2009) for related discussions.…”

“…The aim of this paper is to provide a methodological framework for modeling credit portfolio losses with extreme risks taken into account. Specifically, we employ a static latent variable model recently proposed by Tang and Yuan (2013) for credit portfolio losses, in which the LGD of an obligor is linked to its severity of default through a loss settlement function that increases from 0 to 1 as the severity of default increases. Such a loss settlement function is general in nature, so that the salient features of the LGD distribution found in the empirical studies can easily be incorporated.…”