Related papers: Tail Asymptotics of Deflated Risks
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…
Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and…
In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer…
We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…
Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…
In this paper we establish the error rate of first order asymptotic approximation for the tail probability of sums of log-elliptical risks. Our approach is motivated by extreme value theory which allows us to impose only some weak…
This paper investigates the second order asymptotic expansion for tail probabilities of discounted aggregate claims in continuous-time renewal risk models with constant interest force. Concretely, two types of continuous-time renewal risk…
We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…
Let R be a positive random variable independent of S which is beta distributed. In this paper we are interested on the relation between the distribution function of R and that of RS. For this model we derive first some distributional…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…
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…
This paper focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account. We study the asymptotic behaviour of the ruin probability and the tail probability of the aggregate risk amount.…
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…