基于时间不一致性偏好的连续时间代理模型
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摘要
为了构建一个更合理的最优契约模型,本文在经典的连续时间代理模型中假设委托人的时间偏好是不一致的且是成熟型的,采用拟双曲贴现函数刻画时间不一致性偏好过程.本文研究了委托人的时间偏好不一致性对委托人的值函数和最优薪金支付边界的影响.与经典的连续时间代理模型相比,本文的研究结果表明:成熟型委托人的值函数和最优薪金支付边界随时间不一致性偏好程度增大而降低.也就是说,为了弥补来自时间偏好不一致性的不确定风险,时间不一致性偏好的委托人比时间一致性偏好的委托人倾向于以一个更低的薪金更早地、更频繁地支付给代理人,使代理人更早地如实披露现金流.这表明委托人的时间不一致性偏好对最优契约会产生较大影响.
In order to construct a more reasonable and optimal contract model, this paper assumes that the principal is time-inconsistent preferences and sophisticated in the classical continuous-time agency model,where the hyperbolic-discounting functions characterize time-inconsistent preferences. This paper studies the effect of the principal's time inconsistency on her value function and optimal payoff boundary. Compared with the classical continuous-time agency model, the extended model shows that the sophisticated principal's value function and optimal payoff boundary decrease as the degree of time-inconsistency exaggerates. Namely, to remedy the uncertain risk of the time-inconsistent preference, the time-inconsistent principal tends to pay out lower compensations earlier and more frequently than a time-consistent peer,so that the agent chooses to truthfully report cash flows truthfully earlier. It indicates that the principal's time-inconsistent preferences have a great impact on the optimal contract.
In order to construct a more reasonable and optimal contract model, this paper assumes that the principal is time-inconsistent preferences and sophisticated in the classical continuous-time agency model,where the hyperbolic-discounting functions characterize time-inconsistent preferences. This paper studies the effect of the principal's time inconsistency on her value function and optimal payoff boundary. Compared with the classical continuous-time agency model, the extended model shows that the sophisticated principal's value function and optimal payoff boundary decrease as the degree of time-inconsistency exaggerates. Namely, to remedy the uncertain risk of the time-inconsistent preference, the time-inconsistent principal tends to pay out lower compensations earlier and more frequently than a time-consistent peer,so that the agent chooses to truthfully report cash flows truthfully earlier. It indicates that the principal's time-inconsistent preferences have a great impact on the optimal contract.
引文
[1] DeMarzo P M, Sannikov Y. Optimal security design and dynamic capital structure in a continuous-time agency model[J]. The Journal of Finance, 2006, 61(6):2681-2724.
[2] Sannikov Y. A continuous-time version of the principal-agent problem[J]. The Review of Economic Studies, 2008,75(3):957-984.
[3] DeMarzo P M, Fishman M J, He Z, et al. Dynamic agency and the q theory of investment[J]. The Journal of Finance, 2012, 67(6):2295-2340.
[4]甘柳,杨招军,罗鹏飞.基于跳风险的动态代理与托宾Q理论[J].系统工程理论与实践,2017, 37(8):2033-2042.Gan L, Yang Z J, Luo P F. Dynamic agency and Tobin's Q theory based on jump risk[J]. Systems Engineering—Theory&Practice, 2017, 37(8):2033-2042.
[5] Thaler R. Some empirical evidence on dynamic inconsistency[J]. Economics Letters, 1981, 8(3):201-207.
[6] Ainslie G W. Picoeconomics[M]. Cambridge, UK:Cambridge University Press, 1992.
[7] Loewenstein G F, Prelec D. Preferences for sequences of outcomes[J]. Psychological Review, 1993, 100(1):91-108.
[8] Laibson D. Golden eggs and hyperbolic discounting[J]. The Quarterly Journal of Economics, 1997, 112(2):443-477.
[9] Karp L. Non-constant discounting in continuous time[J]. Journal of Economic Theory, 2004, 132(1):557-568.
[10] Grenadier S R, Wang N. Investment under uncertainty and time-inconsistent preferences[J]. Journal of Financial Economics, 2007, 84(1):2-39.
[11] Zou Z, Chen S, Lei W. Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting[J]. Journal of Mathematical Economics, 2014, 52(5):70-80.
[12] Chen S, Li Z, Zeng Y. Optimal dividend strategies with time-inconsistent preferences[J]. Journal of Economic Dynamics&Control, 2014, 46(C):150-172.
[13] Chen S, Zeng Y, Hao Z. Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramer-Lundberg model[J]. Insurance Mathematics&Economics, 2017, 74:31—45.
[14] Li H, Mu C, Yang J. Optimal contract theory with time-inconsistent preferences[J]. Economic Modelling, 2016,52:519-530.
[15] Liu B, Mu C, Yang J. Dynamic agency and investment theory with time-inconsistent preferences[J]. Finance Research Letters, 2017, 20(2):88-95.
[16]邹自然,陈收,杨艳,等.时间偏好不一致委托代理问题的优化与决策[J].中国管理科学,2013,21(4):27-34.Zou Z R, Chen S, Yang Y, et al. The optimization and decision-making of principal-agent problem based on time-inconsistency preference[J]. Chinese Journal of Management Science, 2013, 21(4):27-34.
[17]李仲飞,陈树敏,曾燕.基于时间不一致性偏好与扩散模型的最优分红策略[J].系统工程理论与实践,2015, 35(7):1633-1645.Li Z F, Chen S M, Zeng Y. Optimal dividend strategy for a diffusion model with time-inconsistent preferences[J].Systems Engineering—Theory&Practice, 2015, 35(7):1633-1645.
[18] Harris C, Laibson D. Instantaneous gratification[J]. The Quarterly Journal of Economics, 2013, 128(1):205-248.
[2] Sannikov Y. A continuous-time version of the principal-agent problem[J]. The Review of Economic Studies, 2008,75(3):957-984.
[3] DeMarzo P M, Fishman M J, He Z, et al. Dynamic agency and the q theory of investment[J]. The Journal of Finance, 2012, 67(6):2295-2340.
[4]甘柳,杨招军,罗鹏飞.基于跳风险的动态代理与托宾Q理论[J].系统工程理论与实践,2017, 37(8):2033-2042.Gan L, Yang Z J, Luo P F. Dynamic agency and Tobin's Q theory based on jump risk[J]. Systems Engineering—Theory&Practice, 2017, 37(8):2033-2042.
[5] Thaler R. Some empirical evidence on dynamic inconsistency[J]. Economics Letters, 1981, 8(3):201-207.
[6] Ainslie G W. Picoeconomics[M]. Cambridge, UK:Cambridge University Press, 1992.
[7] Loewenstein G F, Prelec D. Preferences for sequences of outcomes[J]. Psychological Review, 1993, 100(1):91-108.
[8] Laibson D. Golden eggs and hyperbolic discounting[J]. The Quarterly Journal of Economics, 1997, 112(2):443-477.
[9] Karp L. Non-constant discounting in continuous time[J]. Journal of Economic Theory, 2004, 132(1):557-568.
[10] Grenadier S R, Wang N. Investment under uncertainty and time-inconsistent preferences[J]. Journal of Financial Economics, 2007, 84(1):2-39.
[11] Zou Z, Chen S, Lei W. Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting[J]. Journal of Mathematical Economics, 2014, 52(5):70-80.
[12] Chen S, Li Z, Zeng Y. Optimal dividend strategies with time-inconsistent preferences[J]. Journal of Economic Dynamics&Control, 2014, 46(C):150-172.
[13] Chen S, Zeng Y, Hao Z. Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramer-Lundberg model[J]. Insurance Mathematics&Economics, 2017, 74:31—45.
[14] Li H, Mu C, Yang J. Optimal contract theory with time-inconsistent preferences[J]. Economic Modelling, 2016,52:519-530.
[15] Liu B, Mu C, Yang J. Dynamic agency and investment theory with time-inconsistent preferences[J]. Finance Research Letters, 2017, 20(2):88-95.
[16]邹自然,陈收,杨艳,等.时间偏好不一致委托代理问题的优化与决策[J].中国管理科学,2013,21(4):27-34.Zou Z R, Chen S, Yang Y, et al. The optimization and decision-making of principal-agent problem based on time-inconsistency preference[J]. Chinese Journal of Management Science, 2013, 21(4):27-34.
[17]李仲飞,陈树敏,曾燕.基于时间不一致性偏好与扩散模型的最优分红策略[J].系统工程理论与实践,2015, 35(7):1633-1645.Li Z F, Chen S M, Zeng Y. Optimal dividend strategy for a diffusion model with time-inconsistent preferences[J].Systems Engineering—Theory&Practice, 2015, 35(7):1633-1645.
[18] Harris C, Laibson D. Instantaneous gratification[J]. The Quarterly Journal of Economics, 2013, 128(1):205-248.