Optimal Consumption And Asset Allocation With Model Uncertainty

The rational agent hypothesis under the subjective expected utility theory is often challenged by empirical evidence,and the actual decisions of the representative agent often deviates from the results under rational prediction.In order to explain the difference between theory and practice,modern behavioral finance and decisionmaking theory have found that economic agent often suffers losses due to their own belief distortion or wrong identification of the model.Thus,under the condition of model uncertainty,agents often need to make robust optimization decisions,that is,the optimal decision in the worst case after considering belief distortion.As an important basic decision-making theory in finance and even economics,portfolio theory has important theoretical significance and practical needs to explore the robust optimal investment and consumption rules of economic agents under the framework of model uncertainty.Therefore,based on the theoretical framework of model uncertainty,this paper uses the combination of hypothesis analysis,mathematical transformation,model derivation,parameter calibration,numerical simulation and economic analysis to study the optimal investment and consumption rules for a representative agent and the stochastic process of consumers’ investment and consumption under the state dependent ambiguity aversion function,from the aspects of habit formation,time-inconsistent preferences and pandemic shock.Firstly,from the perspective of internal individual characteristics,consumption preference and time preference are two important dimensions to describe individual preferences.A large number of empirical studies show that the utility transformation of consumers is distorted by the habit formation process,and the subjective discount rate has the law of decreasing time.Therefore,both time-varying time preference and state dependent consumption preference will lead to changes in corresponding decision-making behavior.In order to study the impact of agents’ subjective preference characteristics on their robust investment and consumption rules,and to explore whether agents’ subjective characteristics will distort the impact of model uncertainty on the optimal investment and consumption choices,this paper adds habit formation and time-inconsistent preferences to the robust investment and consumption theory respectively.Under the assumption of habit formation,this paper obtains the semi-closed solution of the robust optimal investment and consumption rules according to the method of dynamic programming.By means of numerical simulation,the optimal portfolio and consumption choices under specific parameter settings and the characteristics of their dynamic processes are obtained.It is found that agent’s habit level will lead to aggressive robust optimal consumption and portfolio choices.At the same time,the impact of model uncertainty on consumption rules will continue to strengthen with the rise of habit level,and the impact on investment rules will continue to weaken with the rise of habit level.In addition,from the perspective of the dynamic process of consumption,this paper provides a theoretical explanation for the“excess-sensitive”and“excess-smoothing”puzzle of consumption from the perspective of model uncertainty and habit formation persistence.From the dynamic process of investment,the value of risk assets has the characteristics of mean recovery with the change of habit level.The ambiguity can accelerate the speed of mean recovery and reduce the volatility of the value of risk assets.Under the assumption of time-inconsistent preferences,according to the hyperbolic discount function,this paper obtains the closed solutions of the optimal robust rules for two kinds of agents(Naive agent and Sophisticated agent).The results show that the optimal portfolio rules in the three cases are unchanged,whether it is time consistent agents,naive or sophisticated agents.The model uncertainty distorts portfolio choice by affecting the agent’s effective risk aversion coefficient,and the inconsistency of time preference will not affect the effect of ambiguity.However,from the perspective of optimal consumption rules,the inconsistency of time preference will significantly stimulate consumption.For sophisticated investors,the effect of model uncertainty on consumption will not be distorted by the time-inconsistent preferences,but for naive agent,the effect of model uncertainty on consumption will weaken with the decrease of additional discount factor and become stronger with the increase of change frequency of time preferences.Secondly,from the external economic environment,COVID-19 has made an immeasurable impact on global economic development and financial markets.The uncertainty of the epidemic development and the impact of the epidemic on asset prices,the uncertainty of the financial market itself and the model uncertainty of investors are intertwined.In order to study the difference in the optimal robust investment and consumption rules between the epidemic economy and normal economy,and whether the epidemic distorts the investment and consumption effect of model uncertainty,this paper constructs an epidemic dynamic evolution and impact model based on the stochastic SIS model in epidemiology.Using stochastic optimal control theory,this paper obtains the optimal robust investment and consumption rules under epidemic economy.The numerical results show that the consumption level under the impact of the epidemic has decreased slightly,but the risky asset investment has shrunk greatly.In addition,in the epidemic economic state,the distortion of model uncertainty on consumption will not be affected by the number of infections,but the impact of model uncertainty on the portfolio will gradually disappear with the increase of infection rates.From the dynamic process of investment and consumption,the sensitivity and volatility of consumption decrease with the increase of infections,but the model uncertainty can curb the decline.The expected growth rate of risk asset value changes in a U-shape with respect to infections,while the volatility changes in an inverted U-shape,which is mainly caused by the joint effects of epidemic infection probability and investors’risk position.The research methods and results of this paper not only enrich the robust investment and consumption choice theory and provide a theoretical explanation for the excess-sensitivity and excess-smoothness characteristics of residents’ consumption,but also have important enlightenment for predicting the investment and consumption behavior under different agent preference characteristics.Especially in the post epidemic era,our results provide a theoretical support for the government mitigation and effective vaccination policies.