Linear Quadratic Mean Field Type Control and Mean Field Games with\n Common Noise, with Application to Production of an Exhaustible Resource

2016/07/07 by P. Jameson Graber, Graber, P. Jameson · 6 citations
Economics, Econometrics and Finance · Physics and Astronomy · #93E20 #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1607.02130

openalex publication_date 2016/07/07 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study a general linear quadratic mean field type control problem and\nconnect it to mean field games of a similar type. The solution is given both in\nterms of a forward/backward system of stochastic differential equations and by\na pair of Riccati equations. In certain cases, the solution to the mean field\ntype control is also the equilibrium strategy for a class of mean field games.\nWe use this fact to study an economic model of production of exhaustible\nresources.\n Keywords: mean field type control, mean field games, linear-quadratic,\noptimal control, riccati equations, exhaustible resource production\n

Citations

• On the interpretation of the Master Equation
• Bellman equation and viscosity solutions for mean-field stochastic control problem
• Mean Field Games and Systemic Risk

Cited by

• Dynamic Data Pricing: A Mean Field Stackelberg Game Approach
• Infinite Horizon Linear Quadratic Mean Field Problems with Common Noise and Regime Switching via Conditional McKean-Vlasov FBSDEs
• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity
• Robust mean-field control under common noise uncertainty
• Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls
• Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Control

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