Abstract
We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading costs, the market clears, and supply meets demand. This problem arises in market economies, including electricity generation from renewable sources in smart grids. Our model includes noise on the supply side, which is counterbalanced on the consumption side by storing energy or reducing the demand according to a dynamic price 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 of a continuum population using optimal control techniques. We include numerical schemes for the price computation in the finite and infinite games, and we illustrate the model using real data.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 188-222 |
| Number of pages | 35 |
| Journal | SIAM Journal on Financial Mathematics |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2023 |
Bibliographical note
Funding Information:*Received by the editors September 2, 2021; accepted for publication (in revised form) September 5, 2022; published electronically February 7, 2023. https://doi.org/10.1137/21M1443923 Funding: The authors were partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452. \dagger CEMSE Division, King Abdullah University of Science and Technology KAUST, Thuwal 23955-6900, Saudi Arabia ([email protected], [email protected], [email protected]). 188
Publisher Copyright:
© 2023 Society for Industrial and Applied Mathematics.
Keywords
- common noise
- Lagrange mulitplier
- mean field games
- price formation
ASJC Scopus subject areas
- Numerical Analysis
- Finance
- Applied Mathematics
