A Double Shot Noise Process and Its Application in Insurance
A Double Shot Noise Process and Its Application in Insurance作者机构:Department of Statistics London School of Economics and Political Science London WC2A 2AE United Kingdom Department of Applied Finance and Actuarial Studies Faculty of Business and Economics Macquarie University Sydney NSW 2109 Australia
出 版 物:《Journal of Mathematics and System Science》 (数学和系统科学(英文版))
年 卷 期:2012年第2卷第2期
页 面:82-93页
学科分类:080705[工学-制冷及低温工程] 0810[工学-信息与通信工程] 07[理学] 070205[理学-凝聚态物理] 08[工学] 0807[工学-动力工程及工程热物理] 081001[工学-通信与信息系统] 0702[理学-物理学]
主 题:Double shot noise process a Cox process stochastic intensity and time value of claims aggregate accumulated/discounted claims.
摘 要:The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments (i.e. means and variances) of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.