Robust Optimal Investment Strategy Selection And Asset Specialization

In the financial market,portfolio,as an effective risk dispersion tool,is very important to investors.The optimal portfolio selection is to explore how rational individual investors or institutional investors can choose the type and quantity of investment varieties in the capital market to achieve the optimal asset allocation of limited resources or wealth over time under uncertain conditions,To optimize the future consumption or wealth of investors to the maximum extent,so as to achieve a balance between maximizing the return of the portfolio and minimizing the risk.In the face of complex and changeable financial market and endless financial products,how to choose financial assets to construct the optimal portfolio has always been the focus of modern finance.In financial practice,it is very difficult to accurately describe the real model of asset prices or the actual data generation process,and model uncertainty is widespread.The risk of financial market and model uncertainty are two major factors that need to be considered in quantitative modeling and decision-making analysis in the field of financial mathematics.How to make investment decisions under the framework of model uncertainty has extremely important theoretical and practical value.In this paper,we first consider the selection of robust optimal investment strategy and asset specialization of fuzzy aversive investors under the mean-variance criterion.Investors worry about the model error and choose the robust optimal investment strategy under the mean-variance criterion.Assuming that investors can manage their risks by investing in one risk-free asset and two risk stocks with correlation,we describe the familiarity of investors with the risks faced by different risk stocks through model uncertainty.By applying Lagrange multiplier method,the classical mean-variance problem is transformed into an unconstrained optimal stochastic control problem,and the corresponding HJB equation is solved to obtain the explicit expression of the investor’s Robust optimal investment strategy and value function.Analyze the impact of model uncertainty on investors’ robust optimal investment strategy.The relationship between the investor’s robust optimal investment strategy and the value function and the main parameters of the model is given by numerical calculation.The research results show that when investors have no specific risk information about risky stocks,they will not take risks to invest their funds in risky stocks,but will only invest in another relatively familiar risky stock and adopt the asset specialization investment strategy.However,when investors are completely unfamiliar with the systematic risks of two risky stocks,but have the unique risk information of two risky stocks,investors will invest their funds in two risky stocks.And when investors are unfamiliar with risky assets,ignoring the uncertainty of the model will bring greater utility losses to investors.Then,this paper also discusses the selection of robust optimal investment strategy and asset specialization of fuzzy aversion investors under the utility maximization goal.Investors still worry about the model error and choose the robust optimal investment strategy under the utility maximization goal.Assuming that investors can manage their risks by investing in one risk-free asset and two risk stocks with correlation,we describe the familiarity of investors with the risks faced by different risk stocks through model uncertainty.By solving the HJB equation satisfied by the value function and the optimal strategy,the explicit solution of the optimal investment strategy and value function of the fuzzy aversive investor under the goal of utility maximization is obtained.The influence of model uncertainty on the investor’s robust optimal investment strategy is analyzed.The relationship between the investor’s robust optimal investment strategy and the value function and the main parameters of the model is given through numerical calculation.The research results show that investors will not invest in risky assets when investors with fuzzy aversion are very unfamiliar with risky assets.When each risky stock contains only unique risks and the unique risks are independent of each other,the optimal investment strategy for each risky asset is only related to its own familiarity with its unique risks,not to the other risky stock.The optimal investment strategy of investors is the minus function of their risk aversion coefficient.When investors are more risk-averse,the utility loss caused by ignoring model uncertainty will be greater.