AI 中文总结
本文研究VaR约束下带期权激励的非凹公司管理，运用凹化、分位数形式与鞅方法推导显式解，分析VaR下限、期权与薪酬对管理者决策及公司价值的影响。
AI 中文摘要
本文研究动态公司风险管理问题，考虑厌恶风险的管理者的决策，这些管理者付出有成本的努力并选择项目风险。当管理者的目标函数为非凹，且包含固定薪酬与期权时，我们研究风险价值（VaR）约束如何影响管理者决策与公司价值分布。通过凹化技术，我们分析目标函数凹包络上的最优期末公司价值；应用分位数形式与鞅方法，可推导出最优努力、期末公司价值及项目选择的显式解。通过细致讨论VaR下限与尾部概率的选择，最优期末公司价值可分为九种情形。与基准情形相比，我们发现受VaR约束的管理者会在不同状态下平滑期末公司价值，在好状态下降低价值，在不利状态下支撑价值。此外，当VaR下限较低或适中时，VaR要求通常会改善下行保护并降低破产概率；但当VaR下限足够高时，它会增加破产概率，并在不利状态下诱发“赌博以求恢复”的行为。敏感性分析表明，更大的管理者努力会一致提升公司价值；更多的激励期权会使管理者更具责任感，进而带来更平滑的跨状态期末公司价值；相反，高固定薪酬会使管理者责任感降低，最终导致公司价值更分散。
英文摘要
This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal terminal firm value on the concave envelope of the objective function. Applying the quantile formulation and the martingale approach, we can derive explicit solutions for optimal effort, terminal firm value, and project choice. The optimal terminal firm value can be divided into nine cases by carefully discussing the choices of VaR floor and tail probability. Compared with the benchmark case, we find that a VaR manager will smooth terminal firm value across states, reducing it in good states while supporting it in adverse states. Moreover, a VaR requirement generally improves downside protection and reduces bankruptcy probability when the VaR floor is low or moderate. However, when the VaR floor is sufficiently high, it can increase bankruptcy probability and induce gambling-for-recovery behavior in adverse states. Our sensitivity analysis indicates that greater managerial effort uniformly improves firm value. Moreover, more incentive options make managers more responsible, leading to a smoother terminal firm value across states. In contrast, a high fixed salary makes the manager less responsible and ultimately causes a more dispersed firm value.
