Under the Knightian uncertainty,this paper constructs the optimal principal(he)-agent(she)contract model based on the principal’s expected profit and the agent’s expected utility function by using the sublinear expe...Under the Knightian uncertainty,this paper constructs the optimal principal(he)-agent(she)contract model based on the principal’s expected profit and the agent’s expected utility function by using the sublinear expectation theory.The output process in the model is provided by the agent’s continuous efforts and the principal cannot directly observe the agent’s efforts.In the process of work,risk-averse agent will have the opportunity to make external choices.In order to promote the agent’s continuous efforts,the principal will continuously provide the agents with consumption according to the observable output process after the probation period.In this paper,the Hamilton–Jacobi–Bellman equation is deduced by using the optimality principle under sublinear expectation while the smoothness viscosity condition of the principal-agent optimal contract is given.Moreover,the continuation value of the agent is taken as the state variable to characterize the optimal expected profit of the principal,the agent’s effort and the consumption level under different degrees of Knightian uncertainty.Finally,the behavioral economics is used to analyze the simulation results.The research findings are that the increasing Knightian uncertainty incurs the decline of the principal’s maximum profit;within the probation period,the increasing Knightian uncertainty leads to the shortening of probation period and makes the agent give higher effort when she faces the outside option;what’s more,after the smooth completion of the probation period for the agent,the agent’s consumption level will rise and her effort level will drop as Knightian uncertainty increasing.展开更多
Recent theoretical developments in economics distinguish between risk and ambiguity(Knightian uncertainty).Using state-of-the-art methods with intraday stock market data from February 1993 to February 2021,we derive f...Recent theoretical developments in economics distinguish between risk and ambiguity(Knightian uncertainty).Using state-of-the-art methods with intraday stock market data from February 1993 to February 2021,we derive financial ambiguity and empirically examine the effect of shocks to it on the price and volatility of crude oil.We provide evidence that ambiguity carries important information about future oil returns and volatility perceived by investors.We validate these results using Granger causality and in-sample and out-of-sample forecasting tests.Our findings reveal that financial ambiguity is a possible factor that explains future drops in oil prices and their increased variability.Our findings will benefit scholars and investors interested in how financial ambiguity shapes short-term oil prices.展开更多
We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a correspondin...We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a corresponding nonlinear expectation on the path space of continuous processes.By a general dynamic programming principle,we link this nonlinear expectation to a variational form of the Kolmogorov equation,where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in.This nonlinear affine process yields a tractable model for Knightian uncertainty,especially for modelling interest rates under ambiguity.We then develop an appropriate Ito formula,the respective term-structure equations,and study the nonlinear versions of the Vasiˇcek and the Cox–Ingersoll–Ross(CIR)model.Thereafter,we introduce the nonlinear Vasicek–CIR model.This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence this approach solves the modelling issue arising with negative interest rates.展开更多
In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited ...In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited for this setting.In the discrete-time case with a finite horizon,we define the value function backward and show that it is the smallest G-supermartingale that dominates the payoff process,ensuring the existence of an optimal stopping time.We then extend these results to both the infinite-horizon case and the continuous-time setting.Moreover,we establish the relationship between the value function and the solution of the reflected backward stochastic differential equation driven by G-Brownian motion.展开更多
基金This research was supported by the National Natural Science Foundation of China(No.71571001).
文摘Under the Knightian uncertainty,this paper constructs the optimal principal(he)-agent(she)contract model based on the principal’s expected profit and the agent’s expected utility function by using the sublinear expectation theory.The output process in the model is provided by the agent’s continuous efforts and the principal cannot directly observe the agent’s efforts.In the process of work,risk-averse agent will have the opportunity to make external choices.In order to promote the agent’s continuous efforts,the principal will continuously provide the agents with consumption according to the observable output process after the probation period.In this paper,the Hamilton–Jacobi–Bellman equation is deduced by using the optimality principle under sublinear expectation while the smoothness viscosity condition of the principal-agent optimal contract is given.Moreover,the continuation value of the agent is taken as the state variable to characterize the optimal expected profit of the principal,the agent’s effort and the consumption level under different degrees of Knightian uncertainty.Finally,the behavioral economics is used to analyze the simulation results.The research findings are that the increasing Knightian uncertainty incurs the decline of the principal’s maximum profit;within the probation period,the increasing Knightian uncertainty leads to the shortening of probation period and makes the agent give higher effort when she faces the outside option;what’s more,after the smooth completion of the probation period for the agent,the agent’s consumption level will rise and her effort level will drop as Knightian uncertainty increasing.
文摘Recent theoretical developments in economics distinguish between risk and ambiguity(Knightian uncertainty).Using state-of-the-art methods with intraday stock market data from February 1993 to February 2021,we derive financial ambiguity and empirically examine the effect of shocks to it on the price and volatility of crude oil.We provide evidence that ambiguity carries important information about future oil returns and volatility perceived by investors.We validate these results using Granger causality and in-sample and out-of-sample forecasting tests.Our findings reveal that financial ambiguity is a possible factor that explains future drops in oil prices and their increased variability.Our findings will benefit scholars and investors interested in how financial ambiguity shapes short-term oil prices.
文摘We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine processes.This is done as follows:given a setof parameters for the process,we construct a corresponding nonlinear expectation on the path space of continuous processes.By a general dynamic programming principle,we link this nonlinear expectation to a variational form of the Kolmogorov equation,where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in.This nonlinear affine process yields a tractable model for Knightian uncertainty,especially for modelling interest rates under ambiguity.We then develop an appropriate Ito formula,the respective term-structure equations,and study the nonlinear versions of the Vasiˇcek and the Cox–Ingersoll–Ross(CIR)model.Thereafter,we introduce the nonlinear Vasicek–CIR model.This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence this approach solves the modelling issue arising with negative interest rates.
基金supported by the Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program(Overseas)(Grant No.2023HWYQ-049)the National Natural Science Foundation of China(Grant No.12301178)+1 种基金the Natural Science Foundation of Shandong Province(Grant No.ZR2022QA022)the Fundamental ResearchFundsfor the Central Universities.
文摘In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited for this setting.In the discrete-time case with a finite horizon,we define the value function backward and show that it is the smallest G-supermartingale that dominates the payoff process,ensuring the existence of an optimal stopping time.We then extend these results to both the infinite-horizon case and the continuous-time setting.Moreover,we establish the relationship between the value function and the solution of the reflected backward stochastic differential equation driven by G-Brownian motion.
