Author
J D Esary
Bio: J D Esary is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 101 citations.
Papers
More filters
TL;DR: In this paper, the authors consider some unresolved relationships among various notions of bivariate dependence and show that for any non-decreasing $f$ and $g$ the associated notions of dependence are associated.
Abstract: We consider some unresolved relationships among various notions of bivariate dependence. In particular we show that $P\lbrack T > t \mid S > s\rbrack \uparrow$ in $s$ (or alternately, $P\lbrack T \leqq t \mid S \leqq s\rbrack \downarrow$ in $s$) implies $S, T$ are associated, i.e. $\operatorname{Cov} \lbrack f(S, T), g(S, T)\rbrack \geqq 0$ for all non-decreasing $f$ and $g$.
105 citations
Cited by
More filters
TL;DR: In this article, a function f(x) defined on X = X 1 × X 2 × × × X n where each X i is totally ordered satisfying f (x ∨ y) f(xi ∧ y) ≥ f(y) f (y), where the lattice operations ∨ and ∧ refer to the usual ordering on X, is said to be multivariate totally positive of order 2 (MTP2).
611 citations
Book•
04 Nov 2005
TL;DR: In this article, the authors provide an essential guide to managing modern financial risk by combining coverage of stochastic order and risk measure theories with the basics of risk management, including dependence concepts and dependence orderings.
Abstract: The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website.
590 citations
TL;DR: The authors show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case.
Abstract: The authors review various facts about copulas linking discrete distributions. They show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case. They highlight some of the dangers and limitations of an undiscriminating transposition of modeling and inference practices from the continuous setting into the discrete one.
427 citations
TL;DR: A new and general numerical method for calculating the appropriate convolutions of a wide range of probability distributions using lower and upper discrete approximations to the quantile function (the quasi-inverse of the distribution function) and has advantages over other methods previously proposed.
398 citations
TL;DR: In this paper, various notions of multivariate negative dependence are introduced and their interrelationship is studied, and examples are given to illustrate these concepts in statistics and probability are given.
Abstract: Various notions of multivariate negative dependence are introduced and their interrelationship is studied. Examples are given to illustrate these concepts. Applications of the results in statistics and probability are given.
219 citations