Research on portfolio model based on backward uncertain differential equations

摘要：

倒向不确定微分方程是由Liu过程驱动的一类特殊的微分方程,研究在不确定环境下为达到未来预期目标,当前时刻应该如何决策以及如何采取行为路径的问题,首先,介绍倒向不确定微分方程的有关理论,并讨论线性倒向不确定微分方程的解,其次,考虑到这个理论适用于金融市场中的投资,建立了基于线性倒向不确定微分方程的不确定投资组合模型.

Beackward uncertain differential eguation is a special kind of differential eguations driven by the Liu process. It studies the issue of how to make decisions and take behavioral paths at the current moment in order to achieve the expected goals in the future under uncertain environment. Firstly, the relevant theory of backward uncertain differential equations is in-troduced and the solution of linear backward uncertain differential equation is given. Secondly, considering that the theory of backward uncertain differential equation is suitable for investment in financial market , an uncertain portfolio model character-ized by linear backward uncertain differential equation is established.

作者:

高采文，张飞宇

Gao Caiwen，Zhang Feiyu

机构地区：

山西大同大学数学与统计学院

引用本文：

高采文，张飞宇。基于倒向不确定微分方程的投资组合模型研究[J].河南师范大学学报(自然科学版),2026,54(1):77-82.(Gao Caiwen,Zhang Feiyu.Research on portfolio model based on backward uncertain differential equations[J].Journal of Henan Normal University(Natural Science Edition),2026,54(1):77-82.

DOI:10.16366/j.cnki.1000-2367.2024.11.20.0001.)

基金：

山西省统计科学研究项目；山西大同大学基础科研计划项目；山西大同大学研究生实践创新项目

关键词：

线性倒向不确定微分方程;Liu过程;投资组合模型

linear backward uncertain differential equations; Liu process; portfolio model

分类号：

O175

基于倒向不确定微分方程的投资组合模型研究.pdf