Viscosity Solutions for Controlled McKean--Vlasov Jump-Diffusions

DOI10.1137/19M1290061zbMath1472.49054arXiv1909.12337OpenAlexW3037345507MaRDI QIDQ3300786

Vincenzo Ignazio, Unnamed Author, Matteo Burzoni, Halil Mete Soner

Publication date: 30 July 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.12337

zbMATH Keywords

optimal controlnonlinear integro-differential equationsprobability measuresviscosity solutionsWasserstein spaceMcKean-Vlasov jump-diffusions

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Integro-partial differential equations (45K05) Diffusion processes (60J60) Optimality conditions for problems involving randomness (49K45) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Viscosity solutions to PDEs (35D40) Jump processes on general state spaces (60J76)

Related Items (17)

McKean-Vlasov optimal control: the dynamic programming principle ⋮ Rate of convergence for particle approximation of PDEs in Wasserstein space ⋮ Finite Dimensional Approximations of Hamilton–Jacobi–Bellman Equations for Stochastic Particle Systems with Common Noise ⋮ Stochastic Fokker–Planck Equations for Conditional McKean–Vlasov Jump Diffusions and Applications to Optimal Control ⋮ Viscosity Solutions for Obstacle Problems on Wasserstein Space ⋮ Quenched mass transport of particles toward a target ⋮ Importance sampling for the empirical measure of weakly interacting diffusions ⋮ Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions ⋮ Optimal control of path-dependent McKean-Vlasov SDEs in infinite-dimension ⋮ Ergodic control of McKean-Vlasov SDEs and associated Bellman equation ⋮ Mean field control and finite agent approximation for regime-switching jump diffusions ⋮ Dynamic Programming Equation for the Mean Field Optimal Stopping Problem ⋮ Hamilton-Jacobi equations for controlled gradient flows: the comparison principle ⋮ Viscosity Solutions for McKean–Vlasov Control on a Torus ⋮ Analysis of the finite-state ergodic master equation ⋮ Itô's formula for flows of measures on semimartingales ⋮ Optimal portfolio choice with path dependent benchmarked labor income: a mean field model

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