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
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
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
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).
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.
