Dynamic agency and Tobin's Q theory based on jump risk

We develop a dynamic agency model which is based on Poisson jump and manager's risk-taking. Firstly, we consider an optimal contract design problem that assumes unobservable effort and risk-taking of agent. Equilibrium evolution of agent's value function is provided by using martingale method. Then we provide sufficient and necessary conditions for incentive compatibility contract. Furthermore, this paper gets the differential equation for the enterprise value where the optimal dynamic investment strategies can be obtained at the same time. Numerical analysis shows that, the opportunity to take risk has negative impact on the equity value and optimal investment. Taking into account punishment cost, shareholders should allow a manager's risk-taking behavior within a certain extent. Finally, the relationships between level of risk-taking and related coefficients are also discussed.

引入刻画企业突发损失的泊松跳和管理者自利冒险行为,构建投资Q理论下的动态代理模型.首先基于管理者不可观测的努力和冒险行为进行最优合同设计,利用鞅方法给出了管理者价值函数的演变方程,得到了合同激励相容的充分必要条件.其次,运用随机控制方法,推导了股东价值满足的微分方程,同时给出了最优动态投资策略.数值分析表明,管理者的冒险行为会导致股东价值损失并使得动态投资降到更低水平,另外限制管理者冒险需要额外的管理成本,股东会在一定的程度上放任管理者的冒险.最后就相关参数与管理者冒险程度之间的关系进行了讨论.