Stochastic Comparisons and Optimal Allocation for Policy Limits and Deductibles

Some new results on allocation of coverage limits and deductibles to mutually independent risks

“…Specifically, we build the most unfavorable allocation of policy limits for risks arrayed in the reversed hazard rate order and the most favorable allocation of deductibles for risks arrayed in the hazard rate order. The present results improve some main results in Lu and Meng (2011) and Hu and Wang (2014) by relaxing the log-concavity of probability density to the logconcavity of distribution function or survival function.…”

“…In a more general setup, we develop the usual stochastic orders on the retained loss, which either generalize or supplement the corresponding results due to Lu andMeng (2011) andWang (2014). Also, the most unfavorable and favorable allocations of coverage limits and deductibles are developed for multiple risks with dominated reversed hazard rates and hazard rates, respectively.…”

Allocations of policy limits and ordering relations for aggregate remaining claims

“…Klugman et al (2004) and Cheung (2007). Using the notion of majorization and various types of stochastic orderings, the above problems have been studied by Cheung (2007), Hua and Cheung (2008a,b), Zhuang et al (2009), Lu and Meng (2011), Xu and Hu (2012) and Hu and Wang (2014). Most of these papers are devoted to the cases when the random variables X i 's are either independent or are comonotonic.…”

“…Therefore, the result of Theorem 2.10 can be applied to this distribution. Hu and Wang (2014) considered independent and non-identical distributed risks which are ordered according to the reversed hazard rate ordering and proved that (1.1) holds if f is log-concave. In the following theorem, it is proved that the same result holds if instead of log-concavity, f is assumed to be a decreasing function.…”

Optimal Allocation of Policy Layers for Exponential Risks

“…Lu and Meng (2011) consider the same problems for the case when the risks are ordered according to the likelihood ratio order and each risk has log-concave density. Hu and Wang (2014) further investigated the optimal allocation of the deductibles and the policy limits and generalized several results of Cheung (2007) and Lu and Meng (2011). Fathi Manesh and Khaledi (2015) and Fathi Manesh et al (2016) recently studied these optimization problems with the assumption that the risks are exchangeable with decreasing joint density function.…”