| 摘要: |
| 本文研究了一个具有随机波动率和一般折现函数的动态投资-消费问题.金融市场由两类资产构成: 一类为无风险资产;另一类为风险资产,其价格过程服从随机波动率模型. 投资者偏好通过指数效用函数建模,而折现函数则由一般非指数型折现函数描述.本文利用正倒向随机微分方程(FBSDE)的方法,获得了开环均衡策略存在的必要条件.进一步地, 在FBSDE解存在的前提下, 本文推导出了开环均衡策略的验证定理. |
| 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 |
| DOI： |
| 分类号:O231.3 |
| 基金项目:国家自然科学基金资助(72210107001);北京市自然科学基金资助(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). |
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| OPEN-LOOP EQUILIBRIUM STRATEGY FOR DYNAMIC INVESTMENT-CONSUMPTION PROBLEM UNDER STOCHASTIC VOLATILITY AND GENERAL DISCOUNT FUNCTIONS |
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RUAN Zhong-jie1, LUO Cui-cui2
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1.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;2.International College, University of Chinese Academy of Sciences, Beijing 100190, China
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| 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. |
| Key words: Stochastic volatility Dynamic investment-consumption problem forward-backward stochastic differential equations (FBSDEs) Open-loop equilibrium strategy |
