This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of s...This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooperative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.展开更多
This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential ra...This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.展开更多
This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose ...This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.展开更多
Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an...Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.展开更多
Incorporating asymmetric cost and benefit of supplying excess liquidity into an otherwise standard time inconsistency model this paper offers an explanation of the excess liquidity and housing price booms recently exp...Incorporating asymmetric cost and benefit of supplying excess liquidity into an otherwise standard time inconsistency model this paper offers an explanation of the excess liquidity and housing price booms recently experienced in China. We find that the central bank's incentive to stimulate eeonomie growth with excess liquidity fuels real estate prices and accelerates inflation bias. Therefore, the central bank should free itself from the pressure to achieve an economic growth rate higher than the potential level and assign an appropriate weight to the real estate price fluctuations in the central bank's objective function, so that the central bank "s policy of stimulating economic growth with excess liquidity can be constrained.展开更多
Due to the non-separability of the variance term,the dynamic mean-variance(MV)portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng(Math Finance 10(3):387-406,2000)and Zhou a...Due to the non-separability of the variance term,the dynamic mean-variance(MV)portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng(Math Finance 10(3):387-406,2000)and Zhou and Li(Appl Math Optim 42(1):19-33,2000)develop the pre-committed optimal policy for such a problem using the embedding method.Following this line of research,researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints,realistic market assumptions and various financial applications.As the principle of optimality no longer holds,the pre-committed policy suffers from the time-inconsistent issue,i.e.,the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t.The time inconsistency of the dynamic MV model has become an important yet challenging research topic.This paper mainly focuses on the multi-period mean–variance(MMV)portfolio optimization problem,reviews the essential extensions and highlights the critical development of time-consistent policies.展开更多
基金the National Natural Science Foundation of China (70602012),Texas Advanced Research Program as well as from the Bush Program in the Economics of Public Policy,the Private Enterprise Research Center, and the Lewis Faculty Fellowship at Texas A & M University
文摘This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooperative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.
基金Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093)。
文摘This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.
基金the National Key R&D Program of China under Grant No.2018YFA0703800the National Natural Science Foundation of China under Grant Nos.61773222,61877057 and 61973172。
文摘This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.
文摘Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.
文摘Incorporating asymmetric cost and benefit of supplying excess liquidity into an otherwise standard time inconsistency model this paper offers an explanation of the excess liquidity and housing price booms recently experienced in China. We find that the central bank's incentive to stimulate eeonomie growth with excess liquidity fuels real estate prices and accelerates inflation bias. Therefore, the central bank should free itself from the pressure to achieve an economic growth rate higher than the potential level and assign an appropriate weight to the real estate price fluctuations in the central bank's objective function, so that the central bank "s policy of stimulating economic growth with excess liquidity can be constrained.
基金partially supported by the National Natural Science Foundation of China(Nos.71971132,61573244,71671106,71971083 and 72171138)by the Key Program of National Natural Science Foundation of China(No.71931004)+2 种基金by Shanghai Institute of International Finance and Economicsby Program for Innovative Research Team of Shanghai University of Finance and Economicsby the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE.
文摘Due to the non-separability of the variance term,the dynamic mean-variance(MV)portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng(Math Finance 10(3):387-406,2000)and Zhou and Li(Appl Math Optim 42(1):19-33,2000)develop the pre-committed optimal policy for such a problem using the embedding method.Following this line of research,researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints,realistic market assumptions and various financial applications.As the principle of optimality no longer holds,the pre-committed policy suffers from the time-inconsistent issue,i.e.,the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t.The time inconsistency of the dynamic MV model has become an important yet challenging research topic.This paper mainly focuses on the multi-period mean–variance(MMV)portfolio optimization problem,reviews the essential extensions and highlights the critical development of time-consistent policies.