Technology Category
Reasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: State EstimationMultiagent Systems: Mechanism Design
Here, there and everywhere: state-dependent time-inconsistent stochastic control
🤖 AI Summary
This study addresses time-inconsistent stochastic control problems in continuous time with state-dependent objectives. To tackle the inconsistency arising from the dependence of the objective functional on the current state, the authors construct—for the first time—a system of backward stochastic differential equations (BSDEs) that provides a probabilistic characterization of equilibrium strategies and the associated value function. This approach extends the theoretical framework for time-inconsistent control problems by establishing a novel BSDE representation specifically tailored to the state-dependent setting. By integrating continuous-time stochastic control with time-inconsistency optimization theory, the work successfully derives a BSDE characterization of the equilibrium value function and demonstrates its validity through an application to a linear–quadratic regulator model.
Technology Category
Application Category
📝 Abstract
This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate the equilibrium value function essential for resolving cases where the present state affecting the target functional triggers the inconsistency. Additionally, the paper offers an application exemplifying this theory through the time-inconsistent linear--quadratic regulator.
Problem
Research questions and friction points this paper is trying to address.
time-inconsistent stochastic control
state-dependent
continuous-time framework
equilibrium value function
backward stochastic differential equations
Innovation
Methods, ideas, or system contributions that make the work stand out.
time-inconsistent control
backward stochastic differential equations
equilibrium value function
state-dependent
linear-quadratic regulator
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