Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control

Anticipation in discrete-time LQ control. I. Open-loop control

Time-Inconsistent Discrete-Time Stochastic Linear-Quadratic Optimal Control: Time-consistent Solutions

In this paper, the time-consistent solutions of a timeinconsistent discrete-time stochastic linear-quadratic optimal control are investigated. Different from the existing literature, the definiteness constraint is not posed on the state and the control weight matrices of the cost functional. Necessary and sufficient conditions are, respectively, obtained to the existence of the open-loop time-c...

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework∗

This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to...

Time-Inconsistent Stochastic Linear-Quadratic Control

Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

Time-consistent Individuals, Time-inconsistent Households

I present a model of consumption and savings for multi-person households in which members are imperfectly altruistic and share wealth. I show that, despite having standard exponential time preferences, the household is time-inconsistent: members save too little and overspend on private consumption goods. Access to private illiquid durable goods can exacerbate overconsumption by providing a way ...