Optimal Investment Decision Of Entrepreneurs Under Uncertain Environment

In practice,moral hazard and adverse selection are ubiquitous and difficult to evaluate objectively.We use Brownian motion to describe the wealth dynamics equation of entrepreneurs and express the impact of productivity on the output process by the entrepreneurs’ efforts and risk control ability.Therefore,the influence of entrepreneurs’ effort and risk control ability on their investment,consumption and portfolio allocation is studied.Considering that the uncertainty of the model itself is essential and irreducible,the investment behavior of entrepreneurs based on q theory under Knight uncertainty is studied.The main work of this paper is to study the impact of effort and risk control ability on investment decisions of entrepreneurial entrepreneurs under Knight uncertainty,which mainly consists of the following contents:The first part is the introduction.Firstly,the background and significance of this paper are expounded.Secondly,the paper sorts out the current situation of relevant research at home and abroad.Finally,the content and structure of the paper are summarized.The second part is studies the wealth of entrepreneurs based on q theory under Knight’s uncertainty.Starting from Knight uncertainty,this part studies the impact of Knight uncertainty on entrepreneurs’ wealth accumulation.Firstly,G-Brownian motion is used to describe the wealth dynamic equation of entrepreneurs,and recursive utility is used to express the value function of entrepreneurs.The financial condition of entrepreneurs is measured by the endogenous liquidity-illiquid wealth ratio W.Secondly,G-Brownian motion under the sublinear expectation framework is used to describe the impact of entrepreneurs on the venture market portfolio and firm production,and then the HJB(Hamilton-Jacobi-Bellman)equation satisfied by the entrepreneur value function in the incomplete market is obtained,and the optimal consumption,investment and market portfolio allocation of entrepreneurs are obtained.Finally,the results are simulated numerically.In the third part,on the basis of the second part,obtains the optimal consumption,investment and market portfolio allocation of entrepreneurs through Knight uncertainty q theory model.Through numerical simulation,the paper analyzes the influence of Knight uncertainty on the optimal investment behavior of entrepreneurs by changing their investment sensitivity,effective risk aversion and market portfolio allocation.In the fourth part,on the basis of the third part,considers the impact of the two factors,the degree of effort and the ability of risk control,on the investment behavior of entrepreneurs.After establishing the model of the problem,MATLAB software is used to simulate the numerical solution.On the basis of the third part,the fifth part considers the impact of inflation risk on the investment behavior of entrepreneurs.The nominal capital stock and nominal liquid wealth are transformed into real capital stock and real liquid wealth through inflation,and then the HJB equation satisfied by entrepreneur value function in incomplete market is obtained.Finally,the impact of expected inflation rate on entrepreneur’s investment and consumption behavior is analyzed by numerical simulation solution.The last part is a summary of the research results,and gives the shortcomings of this study and the aspects that can be improved.