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Mean field approach to stochastic control with partial information.
- Source :
-
ESAIM: Control, Optimisation & Calculus of Variations . 8/24/2021, p1-27. 27p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 12928119
- Database :
- Academic Search Index
- Journal :
- ESAIM: Control, Optimisation & Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 152576260
- Full Text :
- https://doi.org/10.1051/cocv/2021085