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Dynamic Programming for Mean-Field Type Control

Author

Listed:
  • Mathieu Laurière

    (Université Denis Diderot (Paris 7))

  • Olivier Pironneau

    (Université Pierre et Marie Curie (Paris 6))

Abstract

We investigate a model problem for optimal resource management. The problem is a stochastic control problem of mean-field type. We compare a Hamilton–Jacobi–Bellman fixed-point algorithm to a steepest descent method issued from calculus of variations. For mean-field type control problems, stochastic dynamic programming requires adaptation. The problem is reformulated as a distributed control problem by using the Fokker–Planck equation for the probability distribution of the stochastic process; then, an extended Bellman’s principle is derived by a different argument than the one used by P. L. Lions. Both algorithms are compared numerically.

Suggested Citation

  • Mathieu Laurière & Olivier Pironneau, 2016. "Dynamic Programming for Mean-Field Type Control," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 902-924, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-015-0785-x
    DOI: 10.1007/s10957-015-0785-x
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    References listed on IDEAS

    as
    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.
    3. repec:dau:papers:123456789/7431 is not listed on IDEAS
    4. Min Shen & Gabriel Turinici, 2012. "Liquidity generated by heterogeneous beliefs and costly estimations," Post-Print hal-00638966, HAL.
    Full references (including those not matched with items on IDEAS)

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