完备市场和不确定性风险下的养老金投资组合

Pension portfolio under complete market and uncertainty risk

为了更好地契合实际金融市场,同时为模糊厌恶的养老投资者提供最优的投资策略,将价格扩散不确定性、波动扩散不确定性及跳跃过程的不确定性整合到具有罕见事件的传统股票市场中,推导出半封闭形式的稳健动态衍生品投资策略。通过数值分析,得出以下结论:在波动率跳跃幅度较大的情况下,投资者倾向于在负价格跳跃时增加对价格和波动率的风险敞口,并减少对市场跳跃的敞口。股票和波动率风险的最优敞口主要受到投资者对股票价格和波动率风险因素的模糊厌恶的影响,而市场跳跃风险的最优敞口则受到投资者对波动率和罕见事件风险因素的模糊厌恶的显著影响。

To better fit the actual financial market and provide optimal investment strategy for an ambiguity-averse pension investor,we derive a robust dynamic derivative strategies in a semi-closed form by integrating the uncertainty of price diffusion,volatility diffusion and the jump process into the traditional stock market with rare events to capture these events more accurately.Through numerical analysis,we abtain the following conclusions:given a larger volatility jump size,investors tend to increase their exposures to price and volatility and decrease their exposure to market jumps during downward price jumps.In the case of large volatility jumps,investors tend to increase their exposure to prices and volatility,and reduce their exposure to market jumps when prices jump downward decline.The optimal exposures of stocks and volatility risk are most significantly affected by investors ambiguity aversion to stock prices and volatility risk factors,respectively,while the optimal exposure of market jump risk is significantly affected by investors ambiguity aversion to volatility and rare event risk factors.