Some New Results on Policy Limit Allocations

IF 0.1 Q4 STATISTICS & PROBABILITY
Sirous Fathi Manesh, Muhyiddin Izadi, Baha-Eldin Khaledi
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引用次数: 0

Abstract

. Suppose that a policyholder faces n risks X 1 , . . . , X n which are insured under the policy limit with the total limit of l . Usually, the policyholder is asked to protect each X i with an arbitrary limit of l i such that (cid:80) ni = 1 l i = l . If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, we prove that the equal limits provide the maximum of the expected utility of the wealth of policyholder. If the risks with log-concave distribution functions are independent and ordered in the sense of the reversed hazard rate order, we show that the equal limits is the most favourable allocation among the worst allocations. We also prove that if the joint probability density function is arrangement increasing, then the best arranged allocation maximizes the utility expectation of policyholder’s wealth. We apply the main results to the case when the risks are distributed according to a log-normal distribution. MSC: 60E15, 62P05.
关于策略极限分配的一些新结果
. 假设投保人面临n个风险x1,…, X, n,按保单限额投保,总限额为1。通常,保单持有人被要求保护每个X i的任意限制i,使得(cid:80) ni = 1 i = 1。如果风险是独立的、具有对数凹累积分布函数的同分布,我们利用多数化和随机排序的概念,证明了相等的极限提供了投保人财富期望效用的最大值。如果具有对数凹分布函数的风险是独立的,并且在逆向风险率顺序意义上是有序的,我们证明了在最差分配中,相等的限制是最有利的分配。我们还证明了如果联合概率密度函数是排列递增的,那么最优的排列分配使投保人财富的效用期望最大化。我们将主要结果应用于风险按对数正态分布分布的情况。Msc: 60e15, 62p05。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
1.50
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