Setting a proper minimum capital requirement is one of the most fundamental problems in the insurance industry. Ruin theory proposes a solution to this problem by identifying the minimum capital that a company needs to hold in order to stay solvent with a high probability. In this note we discuss the ruin theory risk consistency. More precisely we show that the ruin-consistent Value-at-Risk (VaR) is not continuous in probability, in \(L^{p},0\le p<\infty \), and in weak convergence. Furthermore, it is not a monotone measure of risk.

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破产理论的风险一致性和单调性

设定适当的最低资本要求是保险业最基本的问题之一。废墟理论提出了一个解决方案，即确定公司为了保持较高的偿债能力而需要持有的最低资本。在本文中，我们讨论了破产理论的风险一致性。更准确地说，我们证明了与破产相关的风险价值（VaR）在\（L ^ {p}，0 \ le p <\ infty \）中并且在弱收敛中不是连续的概率。此外，它不是风险的单调度量。