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Volumn 370, Issue 3, 2018, Pages 2115-2160

Randomized dynamic programming principle and feynman-kac representation for optimal control of McKean-Vlasov dynamics

Author keywords

Controlled McKean Vlasov stochastic differential equations; Dynamic programming principle; Forward backward stochastic differential equations; Randomization method

Indexed keywords


EID: 85039799809     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/tran/7118     Document Type: Article
Times cited : (85)

References (32)
  • 1
    • 79958262462 scopus 로고    scopus 로고
    • A maximum principle for SDEs of mean-field type
    • MR2784835
    • Daniel Andersson and Boualem Djehiche, A maximum principle for SDEs of mean-field type, Appl. Math. Optim. 63 (2011), no. 3, 341–356, DOI 10.1007/s00245-010-9123-8. MR2784835
    • (2011) Appl. Math. Optim. , vol.63 , Issue.3 , pp. 341-356
    • Andersson, D.1    Djehiche, B.2
  • 2
    • 84972518057 scopus 로고
    • Extension of uniformly continuous transformations and hyperconvex metric spaces
    • MR0084762
    • N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405–439. MR0084762
    • (1956) Pacific J. Math. , vol.6 , pp. 405-439
    • Aronszajn, N.1    Panitchpakdi, P.2
  • 5
    • 85018981679 scopus 로고    scopus 로고
    • On the interpretation of the Master Equation
    • MR3652408
    • A. Bensoussan, J. Frehse, and S. C. P. Yam, On the interpretation of the Master Equation, Stochastic Process. Appl. 127 (2017), no. 7, 2093–2137. MR3652408
    • (2017) Stochastic Process. Appl , vol.127 , Issue.7 , pp. 2093-2137
    • Bensoussan, A.1    Frehse, J.2    Yam, S.C.P.3
  • 8
    • 80052971337 scopus 로고    scopus 로고
    • A general stochastic maximum principle for SDEs of mean-field type
    • MR2822408
    • Rainer Buckdahn, Boualem Djehiche, and Juan Li, A general stochastic maximum principle for SDEs of mean-field type, Appl. Math. Optim. 64 (2011), no. 2, 197–216, DOI 10.1007/s00245-011-9136-y. MR2822408
    • (2011) Appl. Math. Optim. , vol.64 , Issue.2 , pp. 197-216
    • Buckdahn, R.1    Djehiche, B.2    Li, J.3
  • 9
    • 85017161972 scopus 로고    scopus 로고
    • Mean-field stochastic differential equations and associated PDEs
    • MR3630288
    • Rainer Buckdahn, Juan Li, Shige Peng, and Catherine Rainer, Mean-field stochastic differential equations and associated PDEs, Ann. Probab. 45 (2017), no. 2, 824–878. MR3630288
    • (2017) Ann. Probab. , vol.45 , Issue.2 , pp. 824-878
    • Buckdahn, R.1    Li, J.2    Peng, S.3    Rainer, C.4
  • 12
    • 84919448149 scopus 로고    scopus 로고
    • The master equation for large population equilibriums, Stochastic analysis and applications 2014
    • Springer, Cham
    • René Carmona and François Delarue, The master equation for large population equilibriums, Stochastic analysis and applications 2014, Springer Proc. Math. Stat., vol. 100, Springer, Cham, 2014, pp. 77–128, DOI 10.1007/978-3-319-11292-3_4. MR3332710
    • (2014) Springer Proc. Math. Stat , vol.100 , pp. 77-128
    • Carmona, R.1    Delarue, F.2
  • 13
    • 84947717362 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics
    • MR3395471
    • René Carmona and François Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics, Ann. Probab. 43 (2015), no. 5, 2647–2700, DOI 10.1214/14-AOP946. MR3395471
    • (2015) Ann. Probab. , vol.43 , Issue.5 , pp. 2647-2700
    • Carmona, R.1    Delarue, F.2
  • 14
    • 84876129326 scopus 로고    scopus 로고
    • Control of McKean-Vlasov dynamics versus mean field games
    • MR3045029
    • René Carmona, François Delarue, and Aimé Lachapelle, Control of McKean-Vlasov dynamics versus mean field games, Math. Financ. Econ. 7 (2013), no. 2, 131–166, DOI 10.1007/s11579-012-0089-y. MR3045029
    • (2013) Math. Financ. Econ. , vol.7 , Issue.2 , pp. 131-166
    • Carmona, R.1    Delarue, F.2    Lachapelle, A.3
  • 15
    • 84930019381 scopus 로고    scopus 로고
    • Mean field games and systemic risk
    • MR3325083
    • René Carmona, Jean-Pierre Fouque, and Li-Hsien Sun, Mean field games and systemic risk, Commun. Math. Sci. 13 (2015), no. 4, 911–933, DOI 10.4310/CMS.2015.v13.n4.a4. MR3325083
    • (2015) Commun. Math. Sci. , vol.13 , Issue.4 , pp. 911-933
    • Carmona, R.1    Fouque, J.-P.2    Sun, L.-H.3
  • 16
    • 84964402959 scopus 로고    scopus 로고
    • Backward SDE representation for stochastic control problems with nondominated controlled intensity
    • MR3476636
    • Sébastien Choukroun and Andrea Cosso, Backward SDE representation for stochastic control problems with nondominated controlled intensity, Ann. Appl. Probab. 26 (2016), no. 2, 1208– 1259, DOI 10.1214/15-AAP1115. MR3476636
    • (2016) Ann. Appl. Probab. , vol.26 , Issue.2 , pp. 1208-1259
    • Choukroun, S.1    Cosso, A.2
  • 17
    • 84936768219 scopus 로고    scopus 로고
    • Randomized and backward SDE representation for optimal control of non-Markovian SDEs
    • MR3349004
    • Marco Fuhrman and Huyên Pham, Randomized and backward SDE representation for optimal control of non-Markovian SDEs, Ann. Appl. Probab. 25 (2015), no. 4, 2134–2167, DOI 10.1214/14-AAP1045. MR3349004
    • (2015) Ann. Appl. Probab. , vol.25 , Issue.4 , pp. 2134-2167
    • Fuhrman, M.1    Pham, H.2
  • 18
    • 84860541260 scopus 로고    scopus 로고
    • Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems
    • Wilfrid Gangbo, Hwa Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, Mem. Amer. Math. Soc. 211 (2011), no. 993, vi+77, DOI 10.1090/S0065-9266-2010-00610-0. MR2808856
    • (2011) Mem. Amer. Math. Soc , vol.211 , Issue.993 , pp. 77
    • Gangbo, W.1    Kim, H.K.2    Pacini, T.3
  • 19
    • 0004201402 scopus 로고    scopus 로고
    • 2nd ed., Probability and its Applications (New York), Springer-Verlag, New York
    • Olav Kallenberg, Foundations of modern probability, 2nd ed., Probability and its Applications (New York), Springer-Verlag, New York, 2002. MR1876169
    • (2002) Foundations of Modern Probability
    • Kallenberg, O.1
  • 20
    • 84936797237 scopus 로고    scopus 로고
    • Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps
    • MR3349008
    • Idris Kharroubi, Nicolas Langrené, and Huyên Pham, Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps, Ann. Appl. Probab. 25 (2015), no. 4, 2301–2338, DOI 10.1214/14-AAP1049. MR3349008
    • (2015) Ann. Appl. Probab. , vol.25 , Issue.4 , pp. 2301-2338
    • Kharroubi, I.1    Langrené, N.2    Pham, H.3
  • 21
    • 84930838763 scopus 로고    scopus 로고
    • Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE
    • MR3353816
    • Idris Kharroubi and Huyên Pham, Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE, Ann. Probab. 43 (2015), no. 4, 1823–1865, DOI 10.1214/14-AOP920. MR3353816
    • (2015) Ann. Probab. , vol.43 , Issue.4 , pp. 1823-1865
    • Kharroubi, I.1    Pham, H.2
  • 22
    • 0004275483 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin, 2009. Translated from the 1977 Russian original by A. B. Aries; Reprint of the 1980 edition
    • N. V. Krylov, Controlled diffusion processes, Stochastic Modelling and Applied Probability, vol. 14, Springer-Verlag, Berlin, 2009. Translated from the 1977 Russian original by A. B. Aries; Reprint of the 1980 edition. MR2723141
    • Controlled Diffusion Processes, Stochastic Modelling and Applied Probability , vol.14
    • Krylov, N.V.1
  • 23
    • 85021729169 scopus 로고    scopus 로고
    • Limit theory for controlled McKean-Vlasov dynamics
    • MR3654119
    • Daniel Lacker, Limit theory for controlled McKean-Vlasov dynamics, SIAM J. Control Optim. 55 (2017), no. 3, 1641–1672. MR3654119
    • (2017) SIAM J. Control Optim. , vol.55 , Issue.3 , pp. 1641-1672
    • Lacker, D.1
  • 24
    • 85037625453 scopus 로고    scopus 로고
    • Dynamic programming for mean-field type control (English, with English and French summaries)
    • Mathieu Laurière and Olivier Pironneau, Dynamic programming for mean-field type control (English, with English and French summaries), C. R. Math. Acad. Sci. Paris 352 (2014), no. 9, 707–713, DOI 10.1016/j.crma.2014.07.008. MR3258261
    • (2014) C. R. Math. Acad. Sci. Paris , vol.352 , Issue.9 , pp. 707-713
    • Laurière, M.1    Pironneau, O.2
  • 26
    • 85019004246 scopus 로고    scopus 로고
    • Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics
    • Huyên Pham and Xiaoli Wei, Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics, SIAM J. Control Optim. 55 (2017), no. 2, 1069–1101. MR3631380
    • (2017) SIAM J. Control Optim , vol.55 , Issue.2 , pp. 1069-1101
    • Pham, H.1    Wei, X.2
  • 28
    • 0004225404 scopus 로고    scopus 로고
    • translated from the first (1980) Russian edition by R. P. Boas, Graduate Texts in Mathematics, Springer-Verlag, New York, MR1368405
    • A. N. Shiryaev, Probability, 2nd ed., translated from the first (1980) Russian edition by R. P. Boas, Graduate Texts in Mathematics, vol. 95, Springer-Verlag, New York, 1996. MR1368405
    • (1996) Probability , vol.95
    • Shiryaev, A.N.1
  • 29
    • 0000312906 scopus 로고
    • Calcul stochastique dépendant d’un paramètre
    • MR510530
    • C. Stricker and M. Yor, Calcul stochastique dépendant d’un paramètre (French), Z. Wahrsch. Verw. Gebiete 45 (1978), no. 2, 109–133, DOI 10.1007/BF00715187. MR510530
    • (1978) (French), Z. Wahrsch. Verw. Gebiete , vol.45 , Issue.2 , pp. 109-133
    • Stricker, C.1    Yor, M.2
  • 30
    • 0028500888 scopus 로고
    • Necessary conditions for optimal control of stochastic systems with random jumps
    • MR1288257
    • Shan Jian Tang and Xun Jing Li, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994), no. 5, 1447–1475, DOI 10.1137/S0363012992233858. MR1288257
    • (1994) SIAM J. Control Optim. , vol.32 , Issue.5 , pp. 1447-1475
    • Tang, S.J.1    Li, X.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.