We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same wa...We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.展开更多
基金Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China
文摘We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.
基金Supported by Natural Science Foundation of Jiangxi Province(No.20132BAB211010No.20142BAB211015)+1 种基金Innovation Foundation of Jiangxi Provincial Department of Education,Research Training Program of Nanchang Institute of Technology"Challenge Cup" Academic Science and Technology Work Competition of Nanchang Institute of Technology~~
基金the National Natural Science Foundation of China(Grant Nos.11871121,12271066,12171405)the Shandong Provincial Natural Science Foundation(Grant Nos.ZR2022MG057,ZR2022MG027)。
