Journal ArticleDOI
Some new notions of dependence with applications in optimal allocation problems
Reads0
Chats0
TLDR
This paper proposes several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks.Abstract:
Dependence structures of multiple risks play an important role in optimal allocation problems for insurance, quantitative risk management, and finance. However, in many existing studies on these problems, risks or losses are often assumed to be independent or comonotonic or exchangeable. In this paper, we propose several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks. These characterizations are related to the properties of arrangement increasing functions and the proposed notions of dependence incorporate many typical dependence structures studied in the literature for optimal allocation problems. We also develop the properties of these dependence structures. We illustrate the applications of these notions in the optimal allocation problems of deductibles and policy limits and in capital reserves problems. These applications extend many existing researches to more general dependent risks.read more
Citations
More filters
Journal ArticleDOI
Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks
TL;DR: Property and characterizations of the new dependence notions of LWSAI and WSAI are derived and it is shown that many existing dependence structures are the special cases of these notions of dependence.
Journal ArticleDOI
Allocating active redundancies to k-out-of-n reliability systems with permutation monotone component lifetimes
Yinping You,Rui Fang,Xiaohu Li +2 more
TL;DR: In this article, the authors studied k-out-of-n redundant systems with component lifetimes having lower tail permutation decreasing probability density, and showed that the allocation of a more reliable component to a weaker component is proved to enhance system reliability.
Journal ArticleDOI
Optimal capital allocations to interdependent actuarial risks
Yinping You,Xiaohu Li,Xiaohu Li +2 more
TL;DR: In this article, the authors further studied the capital allocation concerning mutually interdependent random risks and established that risk-averse insurers incline to evenly distribute the total capital among multiple risks.
Journal ArticleDOI
GlueVaR risk measures in capital allocation applications
TL;DR: In this article, two new proportional capital allocation principles based on GlueVaR risk measures are defined and an example based on insurance claims data was presented, in which allocation solutions with tail-subadditive risk measures were discussed.
Journal ArticleDOI
On weighted k-out-of-n systems with statistically dependent component lifetimes
Xiaohu Li,Yinping You,Rui Fang +2 more
TL;DR: For the weighted k-out-of-n system with statistically dependent component lifetimes, a discussion on the system performance through investigating the ordering properties of the total system weight with respect to component weight vector is presented in this article.
References
More filters
Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Book
Actuarial Theory for Dependent Risks: Measures, Orders and Models
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.
Journal ArticleDOI
Optimal Capital Allocation Principles
TL;DR: In this article, a unifying framework for allocating the aggregate capital of a financial firm to its business units is presented, which relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimised.
Journal ArticleDOI
Bivariate characterization of some stochastic order relations
TL;DR: In this paper, the authors provide a general approach that supports the pairwise interchange arguments widely used in various settings, and develop new notions of stochastic order relations so that dependent random variables can be meaningfully compared.
Journal ArticleDOI
Asymptotics for risk capital allocations based on Conditional Tail Expectation
TL;DR: In this article, the authors investigated the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure, with the help of general notions of Extreme Value Theory (EVT).