We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankrup...We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45（4）： 1049-1067].展开更多
基金Acknowledgements The authors would like to thank the anonymous referees for valuable comments and suggestions to improve the earlier version of this paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11401436, 11226204, 11171164, 11271385）, the Doctoral Fund Program of Tianjin Normal University （Grant No. 52XB1204）, and the MOE Youth Project in Humanities and Social Sciences （NO. 14YJCZH048）.
文摘We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45（4）： 1049-1067].
