메뉴 건너뛰기




Volumn 1, Issue 4, 2013, Pages 300-315

A mean-field maximum principle for optimal control of forward–backward stochastic differential equations with Poisson jump processes

Author keywords

Mean field forward backward stochastic differential equation with jump processes; Optimal stochastic control; Poisson martingale measure; Spike variation techniques; Stochastic maximum principle

Indexed keywords

MARKOV PROCESSES; MAXIMUM PRINCIPLE; OPTIMAL CONTROL SYSTEMS; POISSON EQUATION; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

EID: 84975259867     PISSN: 2195268X     EISSN: 21952698     Source Type: Journal    
DOI: 10.1007/s40435-013-0027-8     Document Type: Article
Times cited : (35)

References (29)
  • 1
    • 71249111746 scopus 로고    scopus 로고
    • The maximum principle for fully coupled forward–backward stochastic control system
    • Shi J, Wu Z (2006) The maximum principle for fully coupled forward–backward stochastic control system. Acta Autom Sin 32(2):161–169
    • (2006) Acta Autom Sin , vol.32 , Issue.2 , pp. 161-169
    • Shi, J.1    Wu, Z.2
  • 2
    • 77952008765 scopus 로고    scopus 로고
    • Maximum principle for partially-observed optimal control of fully-coupled forward–backward stochastic systems
    • Shi J, Wu Z (2010) Maximum principle for partially-observed optimal control of fully-coupled forward–backward stochastic systems. J Optim Theory Appl 145(3):543–578
    • (2010) J Optim Theory Appl , vol.145 , Issue.3 , pp. 543-578
    • Shi, J.1    Wu, Z.2
  • 3
    • 0038231628 scopus 로고
    • Stochastic maximum principle for optimal control problem of forward and backward
    • Xu W (1995) Stochastic maximum principle for optimal control problem of forward and backward. J Aust Math Soc Ser B 37:172–185
    • (1995) J Aust Math Soc Ser B , vol.37 , pp. 172-185
    • Xu, W.1
  • 4
    • 0032634560 scopus 로고    scopus 로고
    • Fully coupled forward backward stochastic differential equations and application to optimal control
    • Peng S, Wu Z (1999) Fully coupled forward backward stochastic differential equations and application to optimal control. SIAM J Control Optim 37(3):825–843
    • (1999) SIAM J Control Optim , vol.37 , Issue.3 , pp. 825-843
    • Peng, S.1    Wu, Z.2
  • 5
    • 79955067285 scopus 로고    scopus 로고
    • Optimality variational principle for controlled forward–backward stochastic differential equations with mixed intial-terminal conditions
    • Yong J (2010) Optimality variational principle for controlled forward–backward stochastic differential equations with mixed intial-terminal conditions. SIAM J Control Optim 48(6):4119–4156
    • (2010) SIAM J Control Optim , vol.48 , Issue.6 , pp. 4119-4156
    • Yong, J.1
  • 6
    • 0004254055 scopus 로고    scopus 로고
    • Forward–backward stochastic differential equations and their applications. Lecture notes in mathematics
    • Springer, Berlin
    • Ma J, Yong J (1999) Forward–backward stochastic differential equations and their applications. Lecture notes in mathematics, vol 1702. Springer, Berlin
    • (1999) vol 1702
    • Ma, J.1    Yong, J.2
  • 7
    • 77952417631 scopus 로고    scopus 로고
    • Maximum principle for forward–backward stochastic control system with random jumps and application to finance
    • Shi J, Wu Z (2010) Maximum principle for forward–backward stochastic control system with random jumps and application to finance. J Syst Sci Complex 23:219–231
    • (2010) J Syst Sci Complex , vol.23 , pp. 219-231
    • Shi, J.1    Wu, Z.2
  • 8
    • 37749016692 scopus 로고    scopus 로고
    • Wu Z (2007) Maximum principle for fully coupled Forward-backward stochastic control system with random jumps
    • Hunan, China
    • Shi J, Wu Z (2007) Maximum principle for fully coupled Forward-backward stochastic control system with random jumps. In: Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, China, pp 375–380
    • Proceedings of the 26th Chinese Control Conference, Zhangjiajie , pp. 375-380
    • Shi, J.1
  • 9
    • 84861032958 scopus 로고    scopus 로고
    • Necessary conditions for optimal control of forward–backward stochastic systems with random jumps
    • Shi J (2012) Necessary conditions for optimal control of forward–backward stochastic systems with random jumps. J Stoch Anal 258674:50. doi:10.1155/2012/258674
    • (2012) J Stoch Anal , pp. 50
    • Shi, J.1
  • 10
    • 36248975608 scopus 로고    scopus 로고
    • Discrete time approximation of decoupled forward–backward SDE with jumps
    • Bouchard B, Elie R (2008) Discrete time approximation of decoupled forward–backward SDE with jumps. Stoch Proc Appl 118(1):53–75
    • (2008) Stoch Proc Appl , vol.118 , Issue.1 , pp. 53-75
    • Bouchard, B.1    Elie, R.2
  • 11
    • 0037121523 scopus 로고    scopus 로고
    • A stochastic maximum principle for system with jumps, with applications to finance
    • Cadenillas A (2002) A stochastic maximum principle for system with jumps, with applications to finance. Syst Control Lett 47:433–444
    • (2002) Syst Control Lett , vol.47 , pp. 433-444
    • Cadenillas, A.1
  • 12
    • 4043087607 scopus 로고    scopus 로고
    • Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance
    • Framstad NC, Øksendal B, Sulem A (2004) Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance. J Optim Theory Appl 121:77–98
    • (2004) J Optim Theory Appl , vol.121 , pp. 77-98
    • Framstad, N.C.1    Øksendal, B.2    Sulem, A.3
  • 13
    • 84870378909 scopus 로고    scopus 로고
    • On maximum principle of near-optimality for diffusions with jumps, with application to consumption-investment problem
    • Hafayed M, Veverka P, Abbas S (2012) On maximum principle of near-optimality for diffusions with jumps, with application to consumption-investment problem. Differ Equ Dyn Syst 20(2):111–125
    • (2012) Differ Equ Dyn Syst , vol.20 , Issue.2 , pp. 111-125
    • Hafayed, M.1    Veverka, P.2    Abbas, S.3
  • 16
    • 0010914615 scopus 로고
    • A class of Markov processes associated with nonlinear parabolic equations
    • McKean HP (1966) A class of Markov processes associated with nonlinear parabolic equations. Proc Natl Acad Sci USA 56:1907–1911
    • (1966) Proc Natl Acad Sci USA , vol.56 , pp. 1907-1911
    • McKean, H.P.1
  • 18
    • 39449124383 scopus 로고    scopus 로고
    • Nonlinear diffusion governed by McKean-Vlasov equation on Hilbert space and optimal control
    • Ahmed NU (2007) Nonlinear diffusion governed by McKean-Vlasov equation on Hilbert space and optimal control. SIAM J Control Optim 46:356–378
    • (2007) SIAM J Control Optim , vol.46 , pp. 356-378
    • Ahmed, N.U.1
  • 19
    • 69749102885 scopus 로고    scopus 로고
    • Mean-field backward stochastic differential equations and related partial differential equations
    • Buckdahn R, Li J, Peng S (2009) Mean-field backward stochastic differential equations and related partial differential equations. Stoch Process Appl 119:3133–3154
    • (2009) Stoch Process Appl , vol.119 , pp. 3133-3154
    • Buckdahn, R.1    Li, J.2    Peng, S.3
  • 20
    • 80052971337 scopus 로고    scopus 로고
    • A general stochastic maximum principle for SDEs of mean-field type
    • Buckdahn R, Djehiche B, Li J (2011) A general stochastic maximum principle for SDEs of mean-field type. Appl Math Optim 64:197–216
    • (2011) Appl Math Optim , vol.64 , pp. 197-216
    • Buckdahn, R.1    Djehiche, B.2    Li, J.3
  • 21
    • 70449103246 scopus 로고    scopus 로고
    • Macroscopic limit for stochastic partial differential equations of McKean-Vlasov type
    • Kotelenez PM, Kurtz TG (2010) Macroscopic limit for stochastic partial differential equations of McKean-Vlasov type. Probab Theory Relat Fields 146:189–222
    • (2010) Probab Theory Relat Fields , vol.146 , pp. 189-222
    • Kotelenez, P.M.1    Kurtz, T.G.2
  • 22
    • 84947616476 scopus 로고    scopus 로고
    • A general maximum principle for stochastic differential equations of mean-field type with jump processes
    • Hafayed M, Abbas S (2013) A general maximum principle for stochastic differential equations of mean-field type with jump processes. Technical report
    • (2013) Technical report
    • Hafayed, M.1    Abbas, S.2
  • 24
    • 79958262462 scopus 로고    scopus 로고
    • A maximum principle for SDEs of mean-field type
    • Andersson D, Djehiche B (2011) A maximum principle for SDEs of mean-field type. Appl Math Optim 63:341–356
    • (2011) Appl Math Optim , vol.63 , pp. 341-356
    • Andersson, D.1    Djehiche, B.2
  • 25
    • 84856220494 scopus 로고    scopus 로고
    • Stochastic maximum principle in the mean-field controls
    • Li J (2012) Stochastic maximum principle in the mean-field controls. Automatica 48:366–373
    • (2012) Automatica , vol.48 , pp. 366-373
    • Li, J.1
  • 26
    • 84868330033 scopus 로고    scopus 로고
    • A mean-field stochastic maximum principle via Malliavin calculus
    • Meyer-Brandis T, Øksendal B, Zhou XY (2012) A mean-field stochastic maximum principle via Malliavin calculus. Stochastics. 84(5–6):643–666
    • (2012) Stochastics , vol.84 , Issue.5-6 , pp. 643-666
    • Meyer-Brandis, T.1    Øksendal, B.2    Zhou, X.Y.3
  • 27
    • 84875704848 scopus 로고    scopus 로고
    • A linear-quadratic optimal control problem for mean-field stochastic differential equations
    • Yong J (2011) A linear-quadratic optimal control problem for mean-field stochastic differential equations. Technical report
    • (2011) Technical report
    • Yong, J.1
  • 28
    • 84939984941 scopus 로고    scopus 로고
    • Mean-field forward–backward stochastic differential equations
    • Carmona R, Dularue F (2012) Mean-field forward–backward stochastic differential equations, Technical report
    • (2012) Technical report
    • Carmona, R.1    Dularue, F.2
  • 29
    • 0028500888 scopus 로고
    • Necessary conditions for optimal control of stochastic systems with random jumps
    • Tang SL, Li XJ (1994) Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J Control Optim 32:1447–1475
    • (1994) SIAM J Control Optim , vol.32 , pp. 1447-1475
    • Tang, S.L.1    Li, X.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.