2025/04/01 by Daria Ghilli, Ghilli, Daria, Michele Ricciardi +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #47D03 #49L20 #70H20 #93E20 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2504.00637
openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims to develop a theory for linear-quadratic Nash systems and Master equations in possibly infinite-dimensional Hilbert spaces. As a first step and motivated by the recent results in [31], we study a more general model in the linear quadratic case where the dependence on the distribution enters just in the objective functional through the mean. This property enables the Nash systems and the Master equation to be reduced to two systems of coupled Riccati equations and backward abstract evolution equations. We show that solutions for such systems exist and are unique for all time horizons, a result that is completely new in the literature in our setting. Finally, we apply the results to a vintage capital model, where capital depends on time and age, and the production function depends on the mean of the vintage capital.