TY - JOUR
T1 - Mean Field Control and Finite Agent Approximation for Regime-Switching Jump Diffusions
AU - Bayraktar, Erhan
AU - Cecchin, Alekos
AU - Chakraborty, Prakash
N1 - Funding Information:
E. Bayraktar is supported in part by the National Science Foundation under Grant DMS-2106556 and in part by the Susan M. Smith Professorship.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/10
Y1 - 2023/10
N2 - We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability measures. Using this characterization, we prove that the value function, which is not regular, is the limit of a finite agent centralized optimal control problem as the number of agents go to infinity, with an explicit convergence rate. Assuming in addition that the value function is smooth, we establish a quantitative propagation of chaos result for the optimal trajectory of agent states.
AB - We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability measures. Using this characterization, we prove that the value function, which is not regular, is the limit of a finite agent centralized optimal control problem as the number of agents go to infinity, with an explicit convergence rate. Assuming in addition that the value function is smooth, we establish a quantitative propagation of chaos result for the optimal trajectory of agent states.
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U2 - 10.1007/s00245-023-10015-3
DO - 10.1007/s00245-023-10015-3
M3 - Article
AN - SCOPUS:85160586828
SN - 0095-4616
VL - 88
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
IS - 2
M1 - 36
ER -