Research On Robust Investment Decision-making Behavior In Uncertain Environment

As the former chairman of the Federal Reserve Greenspan pointed out,uncertainty（ambiguity aversion）is regarded by practitioners as the core factor of uncertain events.Uncertainty events are the important source of macroeconomic and financial instability.Uncertain events have occurred continuously in the past two decades,including the 9/11 terrorist attacks,financial crisis,European debt crisis,Brexit,trade war,COVID-19 and so on.Behind these uncertain events,all the ghosts of the crisis are hidden.Faced with these uncertainties,people may lose opportunities to consume,invest,make a profit,or even make a living in an event of this kind.Therefore,the agent needs to make robust and optimal investment decisions under uncertainty.First,this thesis studies how institutional investors invest in the scenario of uncer-tainty.By assuming that a risk-neutral hedge fund manager has ambiguous beliefs about the return process of risky asset,we study the robust risk choice under the high-water mark.The results show that,without management fees,ambiguity aversion induces the fund manager to take more risk as the fund is close to the termination,but to take less risk as the fund approaches the current high-water mark.As management fees increase,the effects of ambiguity aversion following poor performance diminishes.We also con-sider the observational equivalence and nonequivalence in the sense that whether the effects of ambiguity aversion on risk taking can be replicated in quality by other model parameter.Second,this thesis examine the optimal portfolio choice problem with uncertain rare-events risk characterized by ambiguity-price diffusion,volatility diffusion,and jump risk.We first confirm price diffusion ambiguity and jump ambiguity mainly de-termine detection-error probability.Second,we find that the optimal portfolio choice is more significantly affected by price diffusion ambiguity than it is affected by jump am-biguity,and the effect of volatility diffusion is trivial.third,an investor chooses a larger portfolio choice in the market when there is no jump than either upward or downward price jump.Finally,given larger volatility jump size,he gambles by increasing port-folio choice during downward price jump but de-risks by decreasing the choice during upward price jump.Finally,this thesis studies the optimal consumption portfolio problem for an am-biguity averse investor who also has the Liquidity preferences.We establish the Hamiltonian-Jacobi-Bermann-Isaacs（HJBI）equation and get the optimal consumption portfolio under infinite and finite-horizon scenarios,respectively.For an infinite hori-zon scenario,the optimal portfolio is represented by one particular root of the second-order algebraic equation.For the finite horizon scenario,the optimal choice is given by the inverse of the ordinary differential equation solution.We find that the investor’s ambiguity aversion reduces the optimal portfolio,the optimal portfolio decreases with the time,and the Liquidity preferences increases with the time in the finite horizon sce-nario.For recursive utility,we find that the optimal portfolio with Liquidity preferences is not affected by EIS under the same level of ambiguity.An increase in the degree of ambiguity aversion will reduce the optimal portfolio and increase the Liquidity prefer-ences.The goal of this article is to study how to make robust investment decisions in an uncertain environment,and to give an analytical solution to the optimal problem as much as possible,so that the research results can play a good guiding role in invest-ment decisions,for reducing the macroeconomic and financial instability.In order to make the results more intuitive,this article gives some specific numerical analysis to intuitively illustrate the conclusion.