Event
MFG Price Models with Common Noise
Virtual Informal Systems Seminar (VISS), Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)
Zoom Link
Meeting ID: 910 7928 6959
Passcode: VISS
Speaker:
Zoom Link
Meeting ID: 910 7928 6959
Passcode: VISS
Speaker:
Ricardo D. Ribeiro, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (CEMSE-KAUST)
Abstract:
The problem of determining a just price arises in market economies, including electricity generation from renewable sources in smart grids. In this talk, we will review the deterministic MFG price formation model (Gomes-Saúde).
Then we generalize it to an MFG model for the price formation of a commodity whose production is subject to random fluctuations. Here, agents seek to minimize their average cost by choosing their trading rates with a price characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. We show that the optimal trading rates are determined in a feedback form for linear dynamics and quadratic costs. Hence, the price appears as the solution to a stochastic differential equation, whose coefficients depend on a system of ordinary differential equations.Then we consider a discredited version; a finite number of players trade an asset whose supply is a stochastic process. By solving a constrained minimization problem, we prove that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. For the linear-quadratic structure, we characterize the price process using optimal control techniques. We include two numerical approaches for the price computation.
Abstract:
The problem of determining a just price arises in market economies, including electricity generation from renewable sources in smart grids. In this talk, we will review the deterministic MFG price formation model (Gomes-Saúde).
Then we generalize it to an MFG model for the price formation of a commodity whose production is subject to random fluctuations. Here, agents seek to minimize their average cost by choosing their trading rates with a price characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. We show that the optimal trading rates are determined in a feedback form for linear dynamics and quadratic costs. Hence, the price appears as the solution to a stochastic differential equation, whose coefficients depend on a system of ordinary differential equations.Then we consider a discredited version; a finite number of players trade an asset whose supply is a stochastic process. By solving a constrained minimization problem, we prove that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. For the linear-quadratic structure, we characterize the price process using optimal control techniques. We include two numerical approaches for the price computation.
Biography:
Ricardo does research in MFGs and PDEs at the Computer, Electrical and Mathematical Sciences and Engineering at the King Abdullah University of Science and Technology (CEMSE-KAUST) since 2019. Before that he was Professor of Mathematics at UNICAMP (1 year) and UTFPR-Londrina (4 years). He did his PhD under supervision of professors Manuel Valentim Garcia (advisor) and Diogo A. Gomes (co-advisor).