具有随机保费和交易费用的最优投资-再保险策略  

Optimal Investment-Reinsurance Strategy with Stochastic Premium and Transaction Cost

作　　者：杨鹏[1,2] 杜挺 YANG Peng;DU Ting(School of Science,Xijing University,Xi'an 710123,China;School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]西京学院理学院,陕西西安710123 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《应用数学》2021年第1期8-14,共7页Mathematica Applicata

基　　金：西京学院大学生创新创业训练计划项目(X202012715089);陕西省自然科学基础研究计划项目(2020JM-646)。

摘　　要：本文研究具有随机保费和交易费用的最优投资和再保险策略选择问题.保险公司的盈余通过跳-扩散过程来模拟,假设保费收入是随机的.我们的研究目标是寻找一个最优再保险和投资策略,最大化投资终止时刻财富的期望效用.应用随机控制理论,我们得到最优投资-再保险策略和值函数的显式解.通过数值计算,我们给出模型参数对最优策略的影响.结果揭示了一些令人感兴趣的现象,它们可以对实际中的再保险和投资予以指导.This paper studies the optimal investment-reinsurance strategy selection problem with stochastic premium and transaction cost.The surplus of the insurance company is modeled by a jump diffusion process,and we assume that the premium income is stochastic.Our main goal is to find an optimal investment-reinsurance strategy which maximizes the expected utility of the terminal wealth.We obtain closed-form solutions for the optimal investment-reinsurance strategy and the corresponding value function by using the stochastic control theory.We provide the effect of model parameters on the optimal strategy through numerical calculation.The result analyses reveal some interesting phenomena and provide useful guidance for reinsurance and investment in reality.

关 键 词：随机控制 随机保费 交易费用 投资 再保险 

分 类 号：F830[经济管理—金融学] O211[理学—概率论与数理统计]