数学杂志2026，Vol.46Issue(5)：296-310,15.
随机波动率和一般折现函数下动态投资-消费问题的开环均衡解
OPEN-LOOP EQUILIBRIUM STRATEGY FOR DYNAMIC INVESTMENT-CONSUMPTION PROBLEM UNDER STOCHASTIC VOLATILITY AND GENERAL DISCOUNT FUNCTIONS
摘要
Abstract
This paper studies a dynamic investment-consumption problem with stochastic volatility and general discount functions.The financial market consists of two assets:a risk-free asset and a risky asset whose price dynamics follow a stochastic volatility model.The investor's preferences are modeled using an exponential utility function,while future utility is discounted via general non-exponential discount functions.By employing forward-backward stochastic differential equations(FBSDEs),we derive necessary conditions for the existence of an open-loop equilibrium strategy.Furthermore,under the assumption that the FBSDE admits a solution,we establish a verification theorem for the open-loop equilibrium strategy.关键词
随机波动率/动态投资-消费问题/正倒向随机微分方程/开环均衡策略Key words
Stochastic volatility/Dynamic investment-consumption problem/forward-backward stochastic differential equations(FBSDEs)/Open-loop equilibrium strategy分类
数理科学引用本文复制引用
阮中杰,罗翠翠..随机波动率和一般折现函数下动态投资-消费问题的开环均衡解[J].数学杂志,2026,46(5):296-310,15.基金项目
国家自然科学基金资助(72210107001) （72210107001）
北京市自然科学基金资助(IS23128) （IS23128）
中央高校基本科研业务费资助 （）
中国科学院PIFI国际杰出团队项目资助(2024PG0013). （2024PG0013）
