Related papers: Tail Asymptotics of Deflated Risks
We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative…
We consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…
In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic L\'evy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise…
We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows…
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…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
Standard definition of the stochastic Risk-Sensitive Linear-Quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives resolving…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment…
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…
We examine the rate of decay to the limit of the tail dependence coefficient of a bivariate skew t distribution which always displays asymptotic tail dependence. It contains as a special case the usual bivariate symmetric t distribution,…
Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two…
The areas under workload process and under queuing process in a single server queue over the busy period have many applications not only in queuing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
We study the random variables (r.v.) with values in the so-called mixed (anisotropic) Lebesgue-Riesz spaces: formulate the sufficient conditions for belonging of the r.v. to these spaces, estimate the tail of norms distribution, especially…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail…