支付红利时的财富优化模型  

Wealth optimization models for dividends

作　　者：郑颖春[1] 杨云锋[1] ZHENG Ying - chun;YANG Yun - feng(School of Science? X i?an University of Science Technology? X i?an 710054? Shaanxi? China)

机构地区：[1]西安科技大学理学院，陕西 西安 710054

出　　处：《宝鸡文理学院学报（自然科学版）》2016年第2期19-24,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金(71473194);陕西省科技新星计划资助项目(2013XJXX-40)

摘　　要：目的研究跳过程为非爆炸性的计数过程的跳扩散模型下的优化财富问题。方法假定股票只在特定的时间分红,支付的数量等于证券价格的固定比率。利用随机分析的方法确定了唯一的等价鞅测度。结果推广了现有的财富最大化及财富增长率最大化问题的相关结论。结论确定等价鞅测度,给出优化投资组合、优化价值函数及优化财富过程,证明了此唯一的优化投资组合使得财富期望增长率最大。Purposes— To investigate the optimization of wealth under jump-diffusion model which is characterized by non-explosive counting processes.Methods— Suppose that the stock dividends are to be paid at specified times,with the amount of the payment being equal to fixed fraction of the price of the security,the unique equivalent martingale measure is derived on the base of martingale theory and stochastic analysis.Results— The existing conclusions relevant to maximization of wealth and its growth rate are generalized.Conclusions— The optimal wealth process,the value function and the optimal portfolio are gained.The optimal portfolio can maximize wealth growth.

关 键 词：跳扩散过程 等价鞅测度 财富优化 

分 类 号：O211.6[理学—概率论与数理统计]