Related papers: Bounds for randomly shared risk of heavy-tailed lo…
In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…
We model systemic risk using a common factor that accounts for market-wide shocks and a tail dependence factor that accounts for linkages among extreme stock returns. Specifically, our theoretical model allows for firm-specific impacts of…
In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…
In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using…
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account…
Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…
We consider the problem of risk diversification of $\alpha$-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
We introduce a new actuarial tail-shape index, the $\theta$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…