指数谱负Lévy过程下的清算风险  

Liquidation Risk for Exponential Spectrally Negative LéVy Processes

作　　者：李鑫 蒋锋[2] LI Xin;JIANG Feng(School of Finance,Zhongnan University of Economics and Law,Wuhan 430073,China;School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China)

机构地区：[1]中南财经政法大学金融学院,武汉430073 [2]中南财经政法大学统计与数学学院,武汉430073

出　　处：《应用数学学报》2022年第5期732-751,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61773401);中南财经政法大学中央高校基本科研业务费专项资金(2722022BQ015)资助。

摘　　要：在经典破产研究中,许多研究者将盈余过程首次低于某一阈值(通常设置为0)定义为破产事件,这一处理方法简化了研究工作,却忽略了破产事件在现实中的复杂性.Li X,Liu H B,Tang Q H,Zhu J X.Liquidation risk in insurance under contemporary regulatory frameworks.Insurance:Mathematics and Economics,2020,93:36-49采用时齐扩散过程建模保险公司的盈余水平,在考虑破产重整的情况下对保险公司的清算风险进行了概率分析.然而,由于保险公司经营的特殊性,其理赔过程通常是不连续的,需要用带有跳的过程来建模保险公司的盈余过程,另一方面,定义清算事件的三个边界都是正的.考虑到这些因素,本文在指数谱负Lévy过程下对清算风险进行了概率分析.本文通过引入一个辅助盈余过程,将风险模型转化为谱负Levy过程,利用盈余过程的分段强马尔科夫性和谱负Levy过程的波动理论,将清算概率和清算时间的拉普拉斯变换的表达式以scale函数的形式半显示表示.本文最后包含了关于Pareto分布索赔下的数值结果,这在保险研究领域是非常重要的.In classical risk theory,a firm is subject to immediate liquidation when its surplus process drops to an absorbing low barrier.This treatment greatly simplifies research but largely ignores the complexity of the liquidation procedure in the real world.Li X,Liu H B,Tang Q H,Zhu J X.Liquidation risk in insurance under contemporary regulatory frameworks.Insurance:Mathematics and Economics,2020,93:36-49 conducted a probabilistic analysis of the liquidation risk of an insurance company whose surplus process follows timehomogeneous diffusions under the features of reorganization.However,because of insurance companies’ discontinuous claim payments,there is much practical significance to handle the surplus within jump models.Besides,the three barriers applied in the liquidation framework are all positive.Thus,this paper mainly attributes to conduct a probabilistic analysis of the liquidation risk under an exponential spectrally negative Levy process.By introducing an auxiliary surplus process,the risk model is transformed to an spectrally negative Levy process.By applying the piecewise strong Markov property of the surplus process and fluctuation theory of the spectrally negative Levy process,we express the liquidation probability and the Laplace transform of the liquidation time into semi-explicit forms of the scale functions.Finally,we conduct a numerical study incorporating a Pareto distributed claim case which is important in insurance research field.

关 键 词：清算概率 清算时间的拉普拉斯变换 指数谱负Lévy过程 PARETO分布 

分 类 号：O211.9[理学—概率论与数理统计]