Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk
Résumé
We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new infinite-dimensional system of Riccati equations, for which we establish existence and uniqueness. To illustrate our results, we apply this framework to a systemic risk model involving heterogeneous banks, demonstrating the impact of agent heterogeneity on optimal risk mitigation strategies.
Mots clés
- Riccati system
- systemic risk
- Riccati system
- linear quadratic optimal control
- graphons
- heterogeneous interaction
- 93E20 Mean-field SDE
- 49N82
- MSC Classification: 49N10
- MSC Classification: 49N10 49N82 93E20 Mean-field SDE heterogeneous interaction graphons linear quadratic optimal control Riccati system systemic risk
- systemic risk.
- Mean-field SDE
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|---|
| Licence |