Considering that the assumption of time consistency does not adequately reveal the mechanisms of exit decisions of venture capital(VC),this study proposes two kinds of time-inconsistent preferences(i.e.,time-flow inco...Considering that the assumption of time consistency does not adequately reveal the mechanisms of exit decisions of venture capital(VC),this study proposes two kinds of time-inconsistent preferences(i.e.,time-flow inconsistency and time-point incon-sistency)to advance research in this field.Time-flow inconsistency is in line with the previous time inconsistency literature,while time-point inconsistency is rooted in the VC fund’s finite lifespan.Based on the assumption about the strategies guiding future behaviors,we consider four types of venture capitalists:time-consistent,time-point-inconsistent,naïve,and sophisticated venture capitalists,of which the latter three are time-inconsistent.We derive and compare the exit thresholds of these four types of venture capitalists.The main results include:(1)time-inconsistent preferences acceler-ate the exits of venture capitalists;(2)the closer the VC funds expiry dates are,t`he more likely time-inconsistent venture capitalists are to accelerate their exits;and(3)future selves caused by time-flow inconsistency weaken the effect of time-point inconsist-ency.Our study provides a behavioral explanation for the empirical fact of young VCs’grandstanding.展开更多
A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,...A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).展开更多
A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibri...A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.展开更多
Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperati...Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation,and introduce a notion of MP-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.展开更多
Due to bounded rationality, people often rush for instantaneous gratification if the decisions involve immediate rewards, but procrastinate if the decisions involve immediate costs. Present-biased preference and time-...Due to bounded rationality, people often rush for instantaneous gratification if the decisions involve immediate rewards, but procrastinate if the decisions involve immediate costs. Present-biased preference and time-inconsistency will be more salient when people are making inter-temporal decisions to trade off rewards and costs in the future. People outweigh the present and their preference for the outcome in the furore will decline over time. Incorporating present-biased preference and time-inconsistency under quasi-hyperbolic discounting, time value of money under inflation and time-varying demand with shortages completely backlogged, we develop an inventory replenishment model for a deteriorating item. Inventory replenishment policies that benefit the decision maker are as follows. With the increase of time-inconsistency, one can increase ordering number and decrease fraction of shortages; with the increase of hazard rate within an upper limit, one can increase ordering number and decrease fraction of shortage; with the increase of compounded discount rate, one can increase ordering number and fraction of shortage. Hyperbolic discounting increases the ordering number and decreases the final profit, and the degree of hyperbolic discounting strengthens such outcomes. As a result, the optimal policy for a decision maker is to keep as rational as possible when making inter-temporal decisions.展开更多
We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the ...We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.展开更多
In the past decade Chinese inflation was not high on average, but it was quite volatile. Back in the 1980s and 1990s, high inflation was a very real problem. What explains the inflationary dynamics in China？ In parti...In the past decade Chinese inflation was not high on average, but it was quite volatile. Back in the 1980s and 1990s, high inflation was a very real problem. What explains the inflationary dynamics in China？ In particular, does monetary policy account for the substantial run-ups of inflation, followed by the equally substantial dis-inflation？ In the absence of commitment technologies, the monetary authorities may create surprise inflation to achieve higher growth, while private agents would anticipate that and adjust their decisions accordingly, leading to accelerated inflation without a real impact. Do these types of simple time-inconsistency models of monetary policy explain the dynamic pattern of inflation in China？ I show that the long-run and short-run restrictions imposed by discretionary policy, when the time-inconsistent policymaker has a desire to push output above potential, are largely rejected by the data. The estimates of the inflation bias under discretion when the policymaker is asymmetrically averse to recessions are not statistically significant either. The analysis contributes to the understanding of Chinese monetary policy and its inflationary implications and also points to the need of further investigation of inflationary behavior during the economic transition.展开更多
基金supported by the Major Program of the National Social Science Foundation of China under Grant No.17ZDA083the National Natural Science Foundation of China under Grant No.71932002the Natural Science Foundation of Beijing Municipality under Grant No.9192001.
文摘Considering that the assumption of time consistency does not adequately reveal the mechanisms of exit decisions of venture capital(VC),this study proposes two kinds of time-inconsistent preferences(i.e.,time-flow inconsistency and time-point incon-sistency)to advance research in this field.Time-flow inconsistency is in line with the previous time inconsistency literature,while time-point inconsistency is rooted in the VC fund’s finite lifespan.Based on the assumption about the strategies guiding future behaviors,we consider four types of venture capitalists:time-consistent,time-point-inconsistent,naïve,and sophisticated venture capitalists,of which the latter three are time-inconsistent.We derive and compare the exit thresholds of these four types of venture capitalists.The main results include:(1)time-inconsistent preferences acceler-ate the exits of venture capitalists;(2)the closer the VC funds expiry dates are,t`he more likely time-inconsistent venture capitalists are to accelerate their exits;and(3)future selves caused by time-flow inconsistency weaken the effect of time-point inconsist-ency.Our study provides a behavioral explanation for the empirical fact of young VCs’grandstanding.
基金supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011)the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。
文摘A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).
文摘A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
基金supported by the Natural Science Foundation of China under Grant No.11971334.
文摘Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation,and introduce a notion of MP-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.
文摘Due to bounded rationality, people often rush for instantaneous gratification if the decisions involve immediate rewards, but procrastinate if the decisions involve immediate costs. Present-biased preference and time-inconsistency will be more salient when people are making inter-temporal decisions to trade off rewards and costs in the future. People outweigh the present and their preference for the outcome in the furore will decline over time. Incorporating present-biased preference and time-inconsistency under quasi-hyperbolic discounting, time value of money under inflation and time-varying demand with shortages completely backlogged, we develop an inventory replenishment model for a deteriorating item. Inventory replenishment policies that benefit the decision maker are as follows. With the increase of time-inconsistency, one can increase ordering number and decrease fraction of shortages; with the increase of hazard rate within an upper limit, one can increase ordering number and decrease fraction of shortage; with the increase of compounded discount rate, one can increase ordering number and fraction of shortage. Hyperbolic discounting increases the ordering number and decreases the final profit, and the degree of hyperbolic discounting strengthens such outcomes. As a result, the optimal policy for a decision maker is to keep as rational as possible when making inter-temporal decisions.
基金The first author was partially supported by Algerian CNEPRU Project Grant B01420130137,2014-2016.
文摘We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.
文摘In the past decade Chinese inflation was not high on average, but it was quite volatile. Back in the 1980s and 1990s, high inflation was a very real problem. What explains the inflationary dynamics in China？ In particular, does monetary policy account for the substantial run-ups of inflation, followed by the equally substantial dis-inflation？ In the absence of commitment technologies, the monetary authorities may create surprise inflation to achieve higher growth, while private agents would anticipate that and adjust their decisions accordingly, leading to accelerated inflation without a real impact. Do these types of simple time-inconsistency models of monetary policy explain the dynamic pattern of inflation in China？ I show that the long-run and short-run restrictions imposed by discretionary policy, when the time-inconsistent policymaker has a desire to push output above potential, are largely rejected by the data. The estimates of the inflation bias under discretion when the policymaker is asymmetrically averse to recessions are not statistically significant either. The analysis contributes to the understanding of Chinese monetary policy and its inflationary implications and also points to the need of further investigation of inflationary behavior during the economic transition.
