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Volumn 55, Issue 6, 2017, Pages 3833-3868

Mean field games with singular controls

Author keywords

Mean field game; Relaxed control; Singular control; Skorokhod M1 topology

Indexed keywords

MATHEMATICAL TECHNIQUES; OPTIMIZATION;

EID: 85039934437     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/17M1123742     Document Type: Article
Times cited : (48)

References (31)
  • 1
    • 84959878631 scopus 로고    scopus 로고
    • Wellposedness of mean field games with common noise under a weak monotonic-ity condition
    • S. Ahuja, Wellposedness of mean field games with common noise under a weak monotonic-ity condition, SIAM J. Control Optim., 51 (2016), pp. 30-48, https://doi.org/10.1137/ 140974730.
    • (2016) SIAM J. Control Optim. , vol.51 , pp. 30-48
    • Ahuja, S.1
  • 4
    • 84881309217 scopus 로고    scopus 로고
    • Probabilistic analysis of mean-field games
    • R. Carmona and F. Delarue, Probabilistic analysis of mean-field games, SIAM J. Control Optim., 51 (2013), pp. 2705-2734, https://doi.org/10.1137/120883499.
    • (2013) SIAM J. Control Optim. , vol.51 , pp. 2705-2734
    • Carmona, R.1    Delarue, F.2
  • 5
    • 84876129326 scopus 로고    scopus 로고
    • Control of McKean-Vlasov dynamics versus mean field games
    • R. Carmona, F. Delarue, and A. Lachapelle, Control of McKean-Vlasov dynamics versus mean field games, Math. Financ. Econ., 7 (2013), pp. 131-166.
    • (2013) Math. Financ. Econ. , vol.7 , pp. 131-166
    • Carmona, R.1    Delarue, F.2    Lachapelle, A.3
  • 6
    • 85018996101 scopus 로고    scopus 로고
    • Mean field games with common noise
    • R. Carmona, F. Delarue, and D. Lacker, Mean field games with common noise, Ann. Probab., 44 (2016), pp. 3740-3803.
    • (2016) Ann. Probab. , vol.44 , pp. 3740-3803
    • Carmona, R.1    Delarue, F.2    Lacker, D.3
  • 7
    • 84930019381 scopus 로고    scopus 로고
    • Mean field games and systemic risk
    • R. Carmona, J. Fouque, and L. Sun, Mean field games and systemic risk, Commun. Math. Sci., 13 (2015), pp. 911-933.
    • (2015) Commun. Math. Sci. , vol.13 , pp. 911-933
    • Carmona, R.1    Fouque, J.2    Sun, L.3
  • 8
    • 84925426147 scopus 로고    scopus 로고
    • A probabilistic weak formulation of mean field games and ap-plications
    • R. Carmona and D. Lacker, A probabilistic weak formulation of mean field games and ap-plications, Ann. Appl. Probab., 25 (2015), pp. 1189-1231.
    • (2015) Ann. Appl. Probab. , vol.25 , pp. 1189-1231
    • Carmona, R.1    Lacker, D.2
  • 9
    • 84979084054 scopus 로고    scopus 로고
    • A probabilistic approach to mean field games with major and minor players
    • R. Carmona and X. Zhu, A probabilistic approach to mean field games with major and minor players, Ann. Appl. Probab., 26 (2016), pp. 1535-1580.
    • (2016) Ann. Appl. Probab. , vol.26 , pp. 1535-1580
    • Carmona, R.1    Zhu, X.2
  • 10
    • 85031917196 scopus 로고    scopus 로고
    • Fracking, renewables and mean field games
    • P. Chan and R. Sircar, Fracking, renewables and mean field games, SIAM Rev., 59 (2016), pp. 588-615, https://doi.org/10.1137/15M1031424.
    • (2016) SIAM Rev. , vol.59 , pp. 588-615
    • Chan, P.1    Sircar, R.2
  • 12
    • 77958476920 scopus 로고    scopus 로고
    • Mean field games and applications, Paris-Princeton Lectures on Mathematical Finance
    • Springer, Berlin
    • O. Gueant, J. Lasry, and P. Lions, Mean field games and applications, Paris-Princeton Lectures on Mathematical Finance, Lecture Notes in Math. 2003, Springer, Berlin, 2011, pp. 205-266.
    • (2011) Lecture Notes in Math. 2003 , pp. 205-266
    • Gueant, O.1    Lasry, J.2    Lions, P.3
  • 14
    • 0025460639 scopus 로고
    • On the existence of optimal controls
    • U. Haussmann and J. Lepeltier, On the existence of optimal controls, SIAM. J. Control Optim., 28 (1990), pp. 851-902, https://doi.org/10.1137/0328049.
    • (1990) SIAM. J. Control Optim. , vol.28 , pp. 851-902
    • Haussmann, U.1    Lepeltier, J.2
  • 15
    • 0029308403 scopus 로고
    • Singular optimal stochastic controls I: Existence
    • U. Haussmann and W. Suo, Singular optimal stochastic controls I: Existence, SIAM. J. Control Optim., 33 (1995), pp. 916-936, https://doi.org/10.1137/S0363012993250256.
    • (1995) SIAM. J. Control Optim. , vol.33 , pp. 916-936
    • Haussmann, U.1    Suo, W.2
  • 16
    • 84908700007 scopus 로고    scopus 로고
    • When to cross the spread: Trading in two-sided limit order books
    • U. Horst and F. Naujokat, When to cross the spread: Trading in two-sided limit order books, SIAM J. Financial Math., 5 (2014), pp. 278-315, https://doi.org/10.1137/110849341.
    • (2014) SIAM J. Financial Math. , vol.5 , pp. 278-315
    • Horst, U.1    Naujokat, F.2
  • 17
    • 33748053988 scopus 로고    scopus 로고
    • Equilibria in systems of social interactions
    • U. Horst and J. Scheinkman, Equilibria in systems of social interactions, J. Econom. Theory, 130 (2006), pp. 44-77.
    • (2006) J. Econom. Theory , vol.130 , pp. 44-77
    • Horst, U.1    Scheinkman, J.2
  • 18
    • 70349752084 scopus 로고    scopus 로고
    • A limit theorem for systems of social interactions
    • U. Horst and J. Scheinkman, A limit theorem for systems of social interactions, J. Math. Econom., 45 (2009), pp. 609-623.
    • (2009) J. Math. Econom. , vol.45 , pp. 609-623
    • Horst, U.1    Scheinkman, J.2
  • 19
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • M. Huang, R. Malhame, and P. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst., 6 (2006), pp. 221-252.
    • (2006) Commun. Inf. Syst. , vol.6 , pp. 221-252
    • Huang, M.1    Malhame, R.2    Caines, P.3
  • 20
    • 0000555789 scopus 로고
    • Sur un type de convergence intermediaire entre la convergence en loi et la convergence en probabilite, Seminaire de probabilites XV, University of Strasbourg
    • Springer, Berlin, New York
    • J. Jacod and J. Memin, Sur un type de convergence intermediaire entre la convergence en loi et la convergence en probabilite, Seminaire de probabilites XV, University of Strasbourg, Lecture Notes in Math. 850, Springer, Berlin, New York, 1981, pp. 529-546.
    • (1981) Lecture Notes in Math , vol.850 , pp. 529-546
    • Jacod, J.1    Memin, J.2
  • 22
    • 0003242243 scopus 로고
    • Brownian Motion and Stochastic Calculus
    • Springer-Verlag, New York
    • I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Grad. Texts in Math. 113, Springer-Verlag, New York, 1991.
    • (1991) Grad. Texts in Math , vol.113
    • Karatzas, I.1    Shreve, S.E.2
  • 23
  • 24
    • 0001274938 scopus 로고
    • Compactification methods in the control of degenerate diffusions: Existence of an optimal control
    • N. El Karoui, D. Huu Nguyen, and M. Jeanblanc-Picque, Compactification methods in the control of degenerate diffusions: Existence of an optimal control, Stochastics, 20 (1987), pp. 196-219.
    • (1987) Stochastics , vol.20 , pp. 196-219
    • El Karoui, N.1    Huu Nguyen, D.2    Jeanblanc-Picque, M.3
  • 25
    • 84933553528 scopus 로고    scopus 로고
    • Mean field games via controlled martingale problems: Existence of Markovian equilibria
    • D. Lacker, Mean field games via controlled martingale problems: Existence of Markovian equilibria, Stochastic Process. Appl., 125 (2015), pp. 2856-2894.
    • (2015) Stochastic Process. Appl. , vol.125 , pp. 2856-2894
    • Lacker, D.1
  • 26
    • 85021729169 scopus 로고    scopus 로고
    • Limit theory for controlled McKean-Vlasov dynamics
    • D. Lacker, Limit theory for controlled McKean-Vlasov dynamics, SIAM. J. Control Optim., 2 (2017), pp. 1641-1672, https://doi.org/10.1137/16M1095895.
    • (2017) SIAM. J. Control Optim. , vol.2 , pp. 1641-1672
    • Lacker, D.1
  • 27
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • J. Lasry and P. Lions, Mean field games, Jpn. J. Math., 2 (2007), pp. 229-260.
    • (2007) Jpn. J. Math. , vol.2 , pp. 229-260
    • Lasry, J.1    Lions, P.2
  • 28
    • 76449105590 scopus 로고    scopus 로고
    • Continuity of a queueing integral representation in the M1 topology
    • G. Pang and W. Whitt, Continuity of a queueing integral representation in the M1 topology, Ann. Appl. Probab., 20 (2010), pp. 214-237.
    • (2010) Ann. Appl. Probab. , vol.20 , pp. 214-237
    • Pang, G.1    Whitt, W.2
  • 31
    • 0001331327 scopus 로고
    • Generalized curves and the existence of an attained absolute minimum in the cal-culus of variations
    • L. Young, Generalized curves and the existence of an attained absolute minimum in the cal-culus of variations, C. R. Soc. Sci. Letters Varsovie, III, 30 (1937), pp. 212-234
    • (1937) C. R. Soc. Sci. Letters Varsovie, III , vol.30 , pp. 212-234
    • Young, L.1


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