| 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。本文采用正倒向随机微分方程（FBSDE），推导出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，本文给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:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| Open-loop equilibrium strategy for dynamic investment-consumption problem under stochastic volatility and general discount functions. |
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ruanzhongjie1, luocuicui2
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1.中国科学院大学;2.International College, University of Chinese Academy of Sciences
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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 orward-backward stochastic differential equations (FBSDEs) Open-loop equilibrium strategy. |
