In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compo...In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.展开更多
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
The ventilation system plays an essential role in underground workings, and improvements in dilution effect to stochastic methane build-up at cul-de-sac of a coalmine require the installation of mixed ventilation syst...The ventilation system plays an essential role in underground workings, and improvements in dilution effect to stochastic methane build-up at cul-de-sac of a coalmine require the installation of mixed ventilation system. For 4-12-1 I N02.8A centrifugal ventilation fan, the characteristic operating function of its mixed ventilation system is calculated from ventilation quantity and total pressure in the actual working status. At cul-de-sac of the reference coalmine, the evolution of methane concentration is a compound Poisson process and equivalent to a Brownian motion for Gaussian distributed increments. Solution of stochastic differential equation driven by mixed ventilation system, with dilution equation for its closure, provides parameters of mine ventilation system for keeping methane concentration within the permissible limit at cul-de-sac of the reference coalmine. These results intend to shed some light on application of blowing-sucking mixed ventilation systems in underground workings, and establish stochastic trends to consider methane control in coalmines.展开更多
基金Supported by the Natural Science Foundation of China(10071019)
文摘In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.
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.
文摘The ventilation system plays an essential role in underground workings, and improvements in dilution effect to stochastic methane build-up at cul-de-sac of a coalmine require the installation of mixed ventilation system. For 4-12-1 I N02.8A centrifugal ventilation fan, the characteristic operating function of its mixed ventilation system is calculated from ventilation quantity and total pressure in the actual working status. At cul-de-sac of the reference coalmine, the evolution of methane concentration is a compound Poisson process and equivalent to a Brownian motion for Gaussian distributed increments. Solution of stochastic differential equation driven by mixed ventilation system, with dilution equation for its closure, provides parameters of mine ventilation system for keeping methane concentration within the permissible limit at cul-de-sac of the reference coalmine. These results intend to shed some light on application of blowing-sucking mixed ventilation systems in underground workings, and establish stochastic trends to consider methane control in coalmines.
