动态投资组合保险模型优化研究

Study on optimization of dynamic portfolio insurance model

基于Merton(1971)的最优消费和投资组合策略模型,利用无风险资产、风险资产复制卖权的方法,建立连续时间条件下的动态投资组合保险模型.在连续时间条件下,把投资者的个人跨期动态投资组合保险决策问题转换为一个静态的效用最大化问题,解出组合保险者最优财富水平对应的最优策略,比较其与Merton的最优投资消费模型投资策略的异同,结果显示参与保险的投资者最优策略与其所拥有的财富无关,与市场风险相关,即市场风险越高,对投资组合保险的需求越大.

This paper establishes a dynamic portfolio insurance model under the condition of continuous time based on Merton＇ s optimal investment-consumption model, which combined the method of replicating dynamic synthetic put option using risk-free and risk assets. And it transferres the problem of investor＇ s individual inter-temporal dynamic portfolio insurance decision into a problem of static uhility maximization under the condition of continuous time, and gives the optimal capital combination strategies corresponding to the optimal wealth level of the portfolio insurers, and compares the difference of strategies between this model and Merton model. The conclusions show that investors＇ optimal strategies of portfolio insurance are not dependent on their wealth, but market risk. That is to say, the higher the risk is, the more the demand of portfolio insurance is.