基于q-理论的家族企业动态模型

Dynamic Model of Family Business Based on q-theory

本文在不完全市场下,基于托宾q-理论,以最大化企业家的CRRA期望效用为目标,在假设企业资本和生产力均随机的条件下,研究家族企业的动态优化问题,即家族企业在动态经营过程中的生产、消费和投资组合的最优决策问题.利用动态规划原理推导出企业最优决策所满足的HJB方程,并通过企业适用的生产消费均衡理论和风险对冲需求对此HJB方程进行求解,得到家族企业的最优生产、最优消费和最优投资策略.最后选取合适参数对家族企业的最优策略进行数值分析,结果表明了企业的最优策略与其流动性之间的变化关系.

Based on Tobin's q-theoretical model,this paper studies the dynamic opti-mization problem of family business in incomplete market.Under the assumption that enterprise capital and productivity are random,we study the optimization problem to maximize the expected utility of CRRA for entrepreneurs.Besides,the problem refers to the optimal decision making of production,consumption and portfolio during dynamic operation.By the principle of dynamic programming,we derive the HJB equation satis-fied by the enterprise optimal decision.In addition,we solve the HJB equation through the applicable production and consumption equilibrium theory as well as risk hedging demand.Then we get the optimal production,optimal consumption and optimal in-vestment strategy of the family business.Finally,we select appropriate parameters for a numerical analysis of the optimal strategy for family businesses,and illustrate the changing relationship between the optimal strategy and its liquidity.