Constrained Optimal Consumption-portfolio With Uncertain Parameters Over Infinite Horizons

The outbreak of financial crisis makes investors inclined to study more stable investment strategies.In addition,with the continuous development of behavioral finance theory,it has become a new direction to study the influence of behavioral characteristics formed by investors' psychology on portfolio.Based on dynamic programming principle and stochastic analysis theory,this paper studies the optimal consumption-investment strategy of the habit formation model and the consistent performance model under Knight uncertainty.In the first chapter,it briefly introduces the research background,current situation and the main work of this paper.In the second chapter,the optimal investment strategy with habit formation factors under Knight uncertainty is studied.Firstly,we use ?-ignorance fuzzy model to describe the uncertainty of return rate,and then establish the optimal consumption-investment model with habit formation under Knight uncertainty.Secondly,we obtain the explicit solution(see Theorem 2.1)of the model by using the proof theorem.Next,the distribution of the ratio of consumption rate and habit index under the optimal strategy is discussed.Finally,a new explanation for the puzzle of equity premium is provided from the perspective of model uncertainty,and it gives the value range of ?in ?-ignorance ambiguity.In this chapter,the results of Constantinides(1990)and Merton(1971)are generalized.In the third chapter,the optimal investment strategy with consistent performance factors under Knight uncertainty is studied.In Knight uncertain financial market,the optimal consumption investment model is established by using the dynamic wealth constraint to express the consistent demand for performance.With the help of two technical lemmas(Lemma 3.1 and Lemma 3.2),we obtain the explicit solution(see Theorem 3.1)of the optimal strategy,and generalize some conclusions of Chen-Tian(2013).At the end of this chapter,we discuss the relationship between habit formation model and consistent performance model.In the fourth chapter,we summarizes the contents of this paper.