Knight 不确定性是经济数学和金融数学研究领域的前沿与热点问题之一。k-无知模糊模型和 Duffie-Epstein 模糊模型是我国著名金融数学家陈增敬教授和 Epstein, 以及 Duffie-Epstein 基于倒向随机微分方程提出的一种特殊的 Knight不确定性 (生成元 g 刻画模糊)，它们可以帮助解释和分析许多经济金融现象。本项目旨在以g-期望和倒向随机微分方程理论为基础，在连续时间，k-无知模糊模型和 Duffie-Epstein 模糊模型下，研究具有一般效用函数的投资者的最优投资策略的性质；建立与经典情形下 (不含模糊) 最优投资策略之间的联系；研究投资者个人特征 (财富水平、风险厌恶和模糊厌恶) 和市场特征 (无风险利率、超额收益率和波动率) 的每个因素对最优投资策略的比较静态分析；并运用该比较静态分析结果从投资选择的角度解释股票溢价之谜和本土偏好之谜。

Knightian uncertainty is one of the hot areas in the economic and financial mathematics theories. k-ignorance ambiguity model and Duffie-Epstein ambiguity model, proposed by Chen-Epstein and Duffie-Epstein respectively, are two special Knightian uncertainties (ambiguity characterized by generator g) which were introduced via backward stochastic differential equations, and these two models can provide fairly reasonable interpretations for some fascinating puzzles in economic and financial phenomenon. Under the framework of k-ignorance ambiguity and Duffie-Epstein ambiguity in a continuous time model, this project aims at studying the optimal risky demand for the agent with general utility function; establishing the connection with the classical situation (without ambiguity); considering the comparative statics of the optimal risky demand for the agent characteristics (wealth level, risk aversion and ambiguity aversion) and the market parameters (including the risk-free interest rate, the expected return and the volatility). Finally, we will apply our comparative statics results for interpreting the equity premium puzzle and home-bias puzzle.