A maximum principle for SDEs of mean-field type
2011 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 63, no 3, 341-356 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2011. Vol. 63, no 3, 341-356 p.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-13441DOI: 10.1007/s00245-010-9123-8ISI: 000288507800002ScopusID: 2-s2.0-79958262462OAI: oai:DiVA.org:kth-13441DiVA: diva2:325377
QC 20110411 uppdaterad från submitted till published 201104112010-06-182010-06-182011-04-11Bibliographically approved