Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space

Autor:	Bayraktar, Erhan, Cheung, Hang, Ekren, Ibrahim, Qiu, Jinniao, Tai, Ho Man, Zhang, Xin
Rok vydání:	2025
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs Mathematics - Probability 49L25 35Q93 35B51 58E30
Druh dokumentu:	Working Paper
Popis:	In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman equations, in a Crandall-Lions-like framework. We allow the second-order derivative in measure to be state-dependent and thus infinite-dimensional, rather than derived from a finite-dimensional operator, hence the term ''fully''. Our argument leverages the construction of smooth approximations from particle systems developed by Cosso, Gozzi, Kharroubi, Pham, and Rosestolato [Trans. Amer. Math. Soc., 2023], and the compactness argument via penalization of measure moments in Soner and Yan [Appl. Math. Optim., 2024]. Our work addresses unbounded dynamics and state-dependent common noise volatility, and to our knowledge, this is the first result of its kind in the literature. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2501.01612 Zobrazit plný text záznamu View this record from Arxiv