Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Sznitman (1991)
Topics in propagation of chaos
P. Caines, Minyi Huang, R. Malhamé (2006)
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principleCommun. Inf. Syst., 6
N. Framstad, B. Øksendal, A. Sulem (2004)
Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to FinanceJournal of Optimization Theory and Applications, 121
B. Jourdain, S. M'el'eard, W. Woyczynski (2007)
Nonlinear SDEs driven by L\'evy processes and related PDEsarXiv: Probability
Tomas Bjork, Agatha Murgoci (2010)
A General Theory of Markovian Time Inconsistent Stochastic Control ProblemsRisk Management eJournal
S. Mitter, A. Moro (1983)
Nonlinear Filtering and Stochastic Control
F. Chighoub, Boualem Djehiche, B. Mezerdi (2009)
The stochastic maximum principle in optimal control of degenerate diffusions with non-smooth coefficients, 17
L.B. Kantorovich, G.S. Rubinstein (1958)
On the space of completely additive functionsVestn. Leningr. Univ., Mat. Meh. Astron., 13
Suleyman Basak, G. Chabakauri (2009)
Dynamic Mean-Variance Asset AllocationAFA 2009 San Francisco Meetings (Archive)
A.S. Sznitman (1989)
Ecôle de Probabilites de Saint Flour, XIX-1989
R. Buckdahn, Boualem Djehiche, Juan Li, S. Peng (2007)
Mean-field backward stochastic differential equations: A limit approachAnnals of Probability, 37
R. Buckdahn, Juan Li, S. Peng (2007)
Mean-field backward stochastic differential equations and related partial differential equationsStochastic Processes and their Applications, 119
J. Lasry, P. Lions (2007)
Mean field gamesJapanese Journal of Mathematics, 2
J. Yong, X. Zhou (1999)
Stochastic Controls: Hamiltonian Systems and HJB Equations
X. Zhou, Duan Li (2000)
Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ FrameworkApplied Mathematics and Optimization, 42
A. Bensoussan (1982)
Lectures on stochastic control
N.U. Ahmed, X. Ding (2001)
Controlled McKean-Vlasov equationsCommun. Appl. Anal., 5
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2011
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.