Related papers: Precise large deviations of sums of widely depende…
We study tail probabilities via some Gaussian approximations. Our results make refinements to large deviation theory. The proof builds on classical results by Bahadur and Rao. Binomial distributions and their tail probabilities are…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…
In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer's theorem and give en extension to an insurance model with investment in…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.
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…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov.…
We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability…
This article studies asymptotic approximations of ruin probabilities of multivariate random walks with heavy-tailed increments. Under our assumptions, the distributions of the increments are closely connected to multivariate…
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 $[0,\infty)^d$…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…