In:
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, Vol. 27 ( 2021), p. 89-
Abstract:
In our present article, we follow our way of developing mean field type control theory in our earlier works [Bensoussan et 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 Bandini et al. [ Stochastic Process. Appl. 129 (2019) 674–711], which is fundamentally different from our present proposed framework.
Type of Medium:
Online Resource
ISSN:
1292-8119
,
1262-3377
DOI:
10.1051/cocv/2021085
Language:
English
Publisher:
EDP Sciences
Publication Date:
2021
detail.hit.zdb_id:
2032256-2
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