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

作　　者：朱筱宁 潘海峰[1] 费为银[1] 张繁红 ZHU Xiaoning;PAN Haifeng;FEI Weiyin;ZHANG Fanhong(Department of Financial Engineering,Anhui Polytechnic University,Wuhu 241000,China;School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]安徽工程大学金融工程系,安徽芜湖241000 [2]上海财经大学数学学院,上海200433

出　　处：《东华大学学报（自然科学版）》2021年第5期121-127,共7页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金资助项目(71571001);安徽高校自然科学基金重点资助项目(KJ2020A0369);安徽工程大学科研基金资助项目(2020YQQ020,Xjky08201904)。

摘　　要：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.

关 键 词：企业家投资 q-理论 Knight不确定 次线性期望 市场投资组合 HJB方程 

分 类 号：F272[经济管理—企业管理]