Determining the total loss distribution from the moments of the exponential of the compound loss

IF 0.4 4区经济学 Q4 BUSINESS, FINANCE

Journal of Operational Risk Pub Date : 2011-09-01 DOI:10.21314/JOP.2011.096

H. Gzyl

引用次数: 2

Abstract

An important problem in the field of insurance and operational risk is the determination of the distribution function when a compound loss model is used for the total loss. A large variety of methods have been developed for this purpose. Here we explore some mathematical aspects of a method consisting of the reconstruction of the cumulative distribution function or the probability density of the compound loss, based on the knowledge of the Laplace transform of the compound loss, or, equivalently, based on the knowledge of the moments of the exponential of the compound loss. This is particularly useful when analytical models exist for the individual severities and for the frequency of events. In this case the moments are the values of the Laplace transform of the compound severity at integer points.

查看原文本刊更多论文

由复合损耗指数矩确定总损耗分布

在保险和操作风险领域的一个重要问题是，当使用复合损失模型计算全部损失时，如何确定其分布函数。为此目的开发了各种各样的方法。在这里，我们探讨了一种方法的一些数学方面，该方法由累积分布函数或复合损失的概率密度的重建组成，基于复合损失的拉普拉斯变换的知识，或者，等价地，基于复合损失的指数矩的知识。当存在针对个别严重程度和事件频率的分析模型时，这一点特别有用。在这种情况下，矩是复合严重性在整数点处的拉普拉斯变换的值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Operational Risk BUSINESS, FINANCE-

CiteScore

1.00

自引率

40.00%

发文量

期刊介绍： In December 2017, the Basel Committee published the final version of its standardized measurement approach (SMA) methodology, which will replace the approaches set out in Basel II (ie, the simpler standardized approaches and advanced measurement approach (AMA) that allowed use of internal models) from January 1, 2022. Independently of the Basel III rules, in order to manage and mitigate risks, they still need to be measurable by anyone. The operational risk industry needs to keep that in mind. While the purpose of the now defunct AMA was to find out the level of regulatory capital to protect a firm against operational risks, we still can – and should – use models to estimate operational risk economic capital. Without these, the task of managing and mitigating capital would be incredibly difficult. These internal models are now unshackled from regulatory requirements and can be optimized for managing the daily risks to which financial institutions are exposed. In addition, operational risk models can and should be used for stress tests and Comprehensive Capital Analysis and Review (CCAR). The Journal of Operational Risk also welcomes papers on nonfinancial risks as well as topics including, but not limited to, the following. The modeling and management of operational risk. Recent advances in techniques used to model operational risk, eg, copulas, correlation, aggregate loss distributions, Bayesian methods and extreme value theory. The pricing and hedging of operational risk and/or any risk transfer techniques. Data modeling external loss data, business control factors and scenario analysis. Models used to aggregate different types of data. Causal models that link key risk indicators and macroeconomic factors to operational losses. Regulatory issues, such as Basel II or any other local regulatory issue. Enterprise risk management. Cyber risk. Big data.