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 wit...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.展开更多
This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random...This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.展开更多
We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes wit...We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment （CVA） is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.展开更多
文摘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.
基金Supported by the National Social Science Fund of China (Grant No.22BTJ060)the Humanities and Social Sciences Foundation of the Ministry of Education of China (Grant No.20YJA910006)+3 种基金the Natural Science Foundation of Jiangsu Province (Grant No.BK20201396)the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.19KJA180003)the Grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No.HKU17306220)the 333 High Level Talent Training Project of Jiangsu Province。
文摘This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.
基金The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. The research of Yinghui Dong was supported by the Natural Science Foundation of Jiangsu Province （Grant No. BK20170064） and QingLan project. The research of Kam Chuen Yuen was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China （Project No. HKU17329216）, and the CAE 2013 research grant from the Society of Actuaries-any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. The research of Guojing Wang was supported by the National Natural Science Foundation of China （Grant No. 11371274）.
文摘We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment （CVA） is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.
