This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal...

We present a new procedure for detecting multiple additive outliers in GARCH(1,1) models at unknown dates. The outlier candidates are the observations with the largest standardized residual. First, a likelihood-ratio based test determines the presence and timing of an outlier. Next, a second...

We present a new procedure for detecting multiple additive outliers in GARCH(1,1) models at unknown dates. The outlier candidates are the observations with the largest standardized residual. First, a likelihood-ratio based test determines the presence and timing of an outlier. Next, a second...

The limiting distributions of the extremes of mixed exponential distributions and the associated rates of convergence are derived. The practical values of the results are illustrated by a numerical study.

This paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a linear transformation of the data by the precision matrix which incorporates the dependence structure of the variables. The limiting null distribution of the...

Cyber incidents are among the most critical business risks for organisations and can lead to large financial losses. However, previous research on loss modelling is based on unassured data sources because the representativeness and completeness of op-risk databases cannot be assured. Moreover,...

In this paper, we investigate the tail probability of the product X∏i=1nYi, where (X,Y1,…,Yn) follows a multivariate Sarmanov distribution. An explicit asymptotic formula is established for the tail probability of the product when X belongs to the Fréchet, Gumbel, or Weibull max-domain of...

Consider a portfolio of n identically distributed risks with dependence structure modeled by an Archimedean survival copula. Wüthrich (2003) and Alink et al. (2004) proved that the probability of a large aggregate loss scales like the probability of a large individual loss, times a...

Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the...