Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Abstract

Let X λ1 , . . . , X λn be dependent non-negative random variables and Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi 's, with E[I pi ] = p i , i = 1, . . . , n. In actuarial sciences, Y i corresponds to the claim amount in a portfolio of risks.In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters λ 1 , . . . , λ n and p 1 , . . . , p n and the variables in the other set have the parameters λ

Ordering results for smallest claim amounts from two portfolios of risks with dependent heterogeneous exponentiated location-scale claims

“…The following theorems can all be proved by using the idea of Nadeb et al [17] along with the results established here. So, their proofs are not presented for conciseness.…”

“…In the following result, lower and upper bounds of¯1 : ( ) are presented. As the proof is similar to that of Theorem 3.6 of [17] and Theorem 3.11, it is omitted. where¯= (1/ ) =1 and 1: = min{ 1 , .…”

“…In this regard, Balakrishnan et al [1] considered two sets of dependent heterogeneous portfolios and established ordering results between the largest claim amounts. Nadeb et al [17] and Nadeb et al [19] developed stochastic ordering results between the smallest claim amounts as well as the largest claim amounts from two sets of interdependent heterogeneous portfolios. Torrado and Navarro [22] investigated distribution-free comparisons between the extreme claim amounts according to several stochastic orderings when the risks have a fixed dependence structure.…”

Ordering results between the largest claims arising from two general heterogeneous portfolios

“…To the best of our knowledge, stochastic comparisons of the largest claim amounts when random claims have ELS models have not been addressed in the literature so far. However, some generalized models to study ordering properties of extreme order statistics in the context of reliability studies can be found in [7][8][9][10][11]16]. In this paper, we address this problem and derive sufficient conditions for the stochastic comparison of the largest claim amounts in the sense of various stochastic orderings.…”

Stochastic Comparisons of the Smallest Claim Amounts from Two Sets of Independent Portfolios

“…Balakrishnan, Zhang, and Zhao (2018) investigated the comparisons of the largest and the sample range of claim amounts arising from two sets of heterogeneous portfolios in the sense of the usual, the hazard rate and the reversed hazard rate orderings, when the severities in portfolios are independent. Nadeb, Torabi, and Dolati (2020b) worked on the comparisons of the largest claim amounts in two heterogeneous portfolios in the sense of the usual stochastic ordering, when the existing severities in each portfolio are dependent. Barmalzan, Najafabadi, and Balakrishnan (2017) discussed on ordering the largest and smallest claim amounts in the sense of the usual stochastic ordering and the hazard rate ordering when the severities belong to the scale model.…”