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Title: Mean field approach to stochastic control with partial information
In our present article, we follow our way of developing mean field type control theory in our earlier works [Bensoussanet al., Mean Field Games and Mean Field Type Control Theory.Springer, New York (2013)], by first introducing the Bellman and then master equations, the system of Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations, and then tackling them by looking for the semi-explicit solution for the linear quadratic case, especially with an arbitrary initial distribution; such a problem, being left open for long, has not been specifically dealt with in the earlier literature, such as Bensoussan [Stochastic Control of Partially Observable Systems. Cambridge University Press, (1992)] and Nisio [Stochastic control theory: Dynamic programming principle. Springer (2014)], which only tackled the linear quadratic setting with Gaussian initial distributions. Thanks to the effective mean-field theory, we propose a solution to this long standing problem of the general non-Gaussian case. Besides, our problem considered here can be reduced to the model in Bandiniet al.[Stochastic Process. Appl.129(2019) 674–711], which is fundamentally different from our present proposed framework.  more » « less
Award ID(s):
1905449
PAR ID:
10469455
Author(s) / Creator(s):
;
Editor(s):
Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinski, R.; Leugering, G.; Trélat, E.; Zhang, X.
Publisher / Repository:
EDP Sciences
Date Published:
Journal Name:
ESAIM: Control, Optimisation and Calculus of Variations
Volume:
27
ISSN:
1292-8119
Page Range / eLocation ID:
89
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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