A Maximum Principle for SDEs of Mean-Field Type View Full Text


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Article Info

DATE

2011-06

AUTHORS

Daniel Andersson, Boualem Djehiche

ABSTRACT

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. More... »

PAGES

341-356

References to SciGraph publications

  • 1982. Lectures on stochastic control in NONLINEAR FILTERING AND STOCHASTIC CONTROL
  • 2004-04. Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2000-01. Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework in APPLIED MATHEMATICS & OPTIMIZATION
  • 2007-03. Mean field games in JAPANESE JOURNAL OF MATHEMATICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00245-010-9123-8

    DOI

    http://dx.doi.org/10.1007/s00245-010-9123-8

    DIMENSIONS

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