Dynmaic Mean-variance Asset Allocation In Ambiguous Market

There are two different manifestations of the uncertainty of the event.One is about the uncertainty of the event with a probability,that is,randomness;the other is about the uncertainty of the event probability,that is,ambiguity.In the study of risk management,the uncertainty about financial market is mainly focused on randomness.So far,most of asset allocation models take randomness as the uncertainty.We consider that dynamic mean-variance asset allocation in ambiguous markets.Trading may take place continuously in two securities: a riskless bond and a risky stock.Assuming that the stock market is an ambiguous market,but it has two basic states:bull market and bear market.Investor has a subjective probability to predict which basic market would occur,and aims to maximize the expected benefit and minimize the variance in every basic market.So how should the investor allocate asset now?We take the weighted mean-variance of basic market as the utility function of ambiguous market,deriving the time-consistent optimal portfolio strategy and coupled PDEs of the expected return in ambiguous markets,and simulating the result by explicit difference method with CEV model as an example.The numerical results show that our model is meaningful,and the optimal strategy is not a simple weighted value of each optimal strategy in two unambiguous markets.