Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information  

作　　者：Jie XIONG Shuaiqi ZHANG Hui ZHAO Xihuan ZENG 

机构地区：[1]Department of Mathematics, FST, University of Macao, Macao, China [2]School of Economics and Commerce, Guangclong University of Technology,Guangzhou 510520, China [3]Department of Statistics, Hebei University of Technology, Tianjin 300401, China [4]Department of Mathematics, Tianjin University, Tianjin 300072, China [5]Institute of Business Administration, University of Macao, Macao, China

出　　处：《Frontiers of Mathematics in China》2014年第4期965-982,共18页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported in part by FDCT 076/2012/A3, SRG022- FST12-XJ, the Natural Science Foundation of Hebei Province （Grant No. A2014202202）, and the National Natural Science Foundation of China （Grant No. 11301376）.

摘　　要：We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems： the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems： the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.

关 键 词：Inside information INVESTMENT REINSURANCE jump diffusion 

分 类 号：O211.67[理学—概率论与数理统计] F842.3[理学—数学]