The Robust Portfolio Strategy Based On Information Constraints And Model Uncertainty

The capacity of investors to acquire and process information plays an important role in the portfolio selection.Portfolio strategy analysis mainly focuses on how to reasonably allocate the wealth of investors to different investment assets,so as to achieve the purpose of minimizing risks and maximizing returns.With the development of real economy and financial market and the synergy between them,more and more investors enter the financial market with relatively low threshold such as stock market and fund market.Acquiring and processing information can be a key step in constructing a portfolio choice.On the one hand,since investors’ attention is limited,only the focused information can be reflected in the portfolio strategy,namely “investors’ limited attention”.In addition,investors’ limited attention to information will also change the structure of portfolio strategies under different utility functions.On the other hand,the capacity of investors to process information is also limited.In the real market,information transmission is often asynchronous.So investors who acquire new information will make investment decisions by combining new information and historical information.There is competition among fund managers,and this competition is formed in relation to career development and seeking clients.Based on this,this thesis primarily analyzes the optimal strategy of an ambiguity-averse investor in the financial market with limited attention to stock information.Then we consider that the influence of investors’ limited attention on portfolio strategy under the mean variance criterion.This thesis also analyzes the robust optimal portfolio problem of a defined contribution pension(DC)fund manager’s information processing capacity under the background risk,inflation risk.Finally,based on the relative wealth level as the performance standard,the game problem between two competing fund managers is considered,and a Nash equilibrium model is established.Specifical results are as follows:First,the limited attention and ambiguity aversion will affect the optimal strategy and the worst-case distortion,and even affect the variance of the estimation.Investors can obtain additional information related to unobservable stock returns to determine optimal decisions.In the model,this additional information is set as a news signal.Specifically,the optimization problem can be decomposed into three stages.The first stage,we apply the standard Kalman filter to estimate the optimal dynamics of stock returns under the framework of the model of investors’ limited attention to the additional signal,and obtain the estimation process.Next,we consider this estimation process as a reference model for a robust optimal control problem.We then construct the penalty function.The worst-case scenario is found by the first order condition.Last,the analytic solution of robust optimization problem is derived by stochastic dynamic programming.Otherwise,we consider a special case and discuss the differences between the general model of limited attention and the special case that does not take into account the investor’s attention.Second,we model the investors’ limited attention under the mean variance criterion and obtain the time-consistent investment strategy.We assume that investors are trading continuously in a financial market consisting of a risky asset and a risk-free asset.Investors have easy access to historical data on stocks,but stock returns are unobservable.She can only get some additional information about return through her limited attention.Kalman filter technology is used to estimate the unobservable variables.In this vein,we can turn the problem into the complete information case.Furthermore,in the framework of game theory,by solving the extended HJB equation,we get the time-consistent investment strategy,the corresponding value function and the effective frontier.Finally,we use numerical examples to verify our theoretical results.Third,better information processing skills can improve a fund manager’s performance and accumulate more money for the pension account.The manager will perform well during market turbulence due to preference for robustness.When the fund manager of DC Pension faces model uncertainty,she will use all her information processing capacity to infer unobservable variables and choose robust strategies.Under the coefficient of relative risk aversion(CRRA)utility,we get the HJB equation by using the principle of dynamic programming.By solving the HJB equation,we obtain the explicit form of robust optimal strategy.Finally,a numerical example is given to analyze the effects of each parameter on strategy and utility loss.Fourth,the difference in information processing capacity will affect the portfolio decisions of two fund managers.We model the case of exponential utility and power utility respectively and get analytical solutions for both.The analytical solution of exponential utility is simple and concise.It is basically divided into the fund manager’s own part and the part related to competitors’ stock strategies,and the fund manager’s own part is divided into the risk investment term and the hedge term.The power utility case is complicated.Firstly,the structure of the optimization problem becomes complicated because our model takes the predictability of return into account.Moreover,the fund manager’s investment also depends on the competitor’s strategy,so the solution becomes very complicated.By introducing the dynamics of relative wealth and applying the dynamic programming principle,we prove that the optimal investment strategy under the predictable return can be represented by the HJB equation.We find an explicit solution of the equation,which enables us to study the equilibrium strategy and the corresponding value function.