arXiv subjects

Ivan Romanò

Publications and source records attributed to Ivan Romanò.

2 recordsLinked to original sources

arXiv2026

The petrol station game: the regional average price. A mean field analysis

In January 2023, the obligation for petrol stations to display the average fuel price calculated on a regional basis was introduced by the Italian Government. A mean field game model is here proposed to describe the evolution of the fuel price. In particular, each petrol station decides its own price, for the next day, taking account of an estimate of the average price, to be communicated by the Local Authority. The existence and the evolution of a mean field equilibrium are analytically investigated. Some simulations are compared with real data from the Autonomous Province of Trento, Italy.

math.OC↗

arXiv2026

State-constrained optimal control of the continuity equation and infinite-dimensional viscosity solutions

We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant compact subset, we prove that the value function is Lipschitz continuous and satisfies, by dynamic programming, the associated infinite dimensional constrained Hamilton Jacobi Bellman equation in viscosity sense (subsolution in the interior, supersolution up to the boundary). We finally prove a comparison principle and uniqueness in the Lipschitz class.

math.OC↗