Knight不确定下基于q-理论的企业家投资行为

Entrepreneurs investment behavior based on q-theory under Knight uncertainty

考虑到模型本身的不确定性是本质的、不可消除的,研究Knight不确定下基于q-理论的创业企业家的投资行为。利用G-布朗运动刻画企业家的财富动力学方程,采用递归效用表示企业家价值函数。用内生的流动财富非流动财富比率测度企业家的财务状况,运用次线性期望框架下的G-布朗运动刻画企业家在风险市场投资组合和公司生产的冲击,得到非完备市场下企业家价值函数满足的HJB(Hamilton-Jacobi-Bellman)方程,并求得企业家的最优消费、投资和市场投资组合配置。通过MATLAB软件模拟数值解,分析Knight不确定通过改变企业家的投资灵敏度、有效风险规避和市场投资组合配置,从而对创业企业家最优投资行为产生的影响。结果表明,不完备市场情形下Knight不确定性越大,企业家的市场投资组合配置比例越小。

The investment behavior of entrepreneurs based on q-theory under Knight uncertainty is studied considering that the uncertainty in the model is intrinsic and non-eliminable.The G-Brownian motion was used to inscribe the entrepreneur s wealth dynamics equation,and the recursive utility was used to represent the entrepreneurial value function.The endogenous liquid-illiquid wealth ratio was used to measure the financial status of the entrepreneur,and the G-Brownian motion in the sublinear expectation framework was used to characterize the entrepreneur s portfolio and firm production shocks in the venture market.The HJB(Hamilton-Jacobi-Bellman)equation satisfied by the entrepreneur s value function in a non-complete market was obtained,as well as the entrepreneur s optimal consumption,investment,and market portfolio allocations.The numerical solution was simulated by MATLAB software to analyze the effect of Knight uncertainty on the entrepreneur s optimal investment behavior by changing the entrepreneur s investment sensitivity,effective risk aversion,and market portfolio allocation.The results show that the greater the Knight uncertainty in the incomplete market scenario,the smaller the market portfolio allocation ratio of entrepreneurs.