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Volumn 41, Issue 4, 2003, Pages 1015-1041

A leader-follower stochastic linear quadratic differential game

Author keywords

Forward backward stochastic differential equation; Leader follower stochastic differential game; Linear quadratic optimal control problem; Stochastic Riccati equation

Indexed keywords

MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; RANDOM PROCESSES; RICCATI EQUATIONS;

EID: 0042928469     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901391925     Document Type: Article
Times cited : (172)

References (34)
  • 1
    • 0043156612 scopus 로고
    • Dynamic Noncooperative Game Theory
    • Philadelphia
    • T. BASAR AND G. J. OLSDER, Dynamic Noncooperative Game Theory, SIAM, Philadelphia, 1995.
    • (1995) SIAM
    • Basar, T.1    Olsder, G.J.2
  • 2
    • 0001475203 scopus 로고
    • Points de Nash dans le cas de fonctionnelles quadratiques et jeux differentiels lineaires a N personnes
    • A. BENSOUSSAN, Points de Nash dans le cas de fonctionnelles quadratiques et jeux differentiels lineaires a N personnes, SIAM J. Control, 12 (1974), pp. 460-499.
    • (1974) SIAM J. Control , vol.12 , pp. 460-499
    • Bensoussan, A.1
  • 3
    • 0002193618 scopus 로고
    • A differential game with no pure strategy
    • Princeton University Press, Princeton, NJ
    • L. D. BERKOVITZ, A differential game with no pure strategy, in Advances in Game Theory, Ann. of Math. Stud. 52, Princeton University Press, Princeton, NJ, 1964, pp. 175-194.
    • (1964) Advances in Game Theory, Ann. of Math. Stud. , vol.52 , pp. 175-194
    • Berkovitz, L.D.1
  • 4
    • 0022028477 scopus 로고
    • The existence of value and saddle point in games of fixed duration
    • L. D. BERKOVITZ, The existence of value and saddle point in games of fixed duration, SIAM J. Control Optim., 23 (1985), pp. 172-196.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 172-196
    • Berkovitz, L.D.1
  • 5
    • 0016949806 scopus 로고
    • Linear quadratic optimal stochastic control with random coefficients
    • J.-M. BISMUT, Linear quadratic optimal stochastic control with random coefficients, SIAM J. Control Optim., 14 (1976), pp. 419-444.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 419-444
    • Bismut, J.-M.1
  • 6
    • 0032165503 scopus 로고    scopus 로고
    • Stochastic linear quadratic regulators with indefinite control weight costs
    • S. CHEN, X. LI, AND X. Y. ZHOU, Stochastic linear quadratic regulators with indefinite control weight costs, SIAM J. Control Optim., 36 (1998), pp. 1685-1702.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1685-1702
    • Chen, S.1    Li, X.2    Zhou, X.Y.3
  • 7
    • 0034415498 scopus 로고    scopus 로고
    • Stochastic linear quadratic optimal control problems with random coefficients
    • S. CHEN AND J. YONG, Stochastic linear quadratic optimal control problems with random coefficients, Chinese Ann. Math. Ser. B, 21 (2000), pp. 323-338.
    • (2000) Chinese Ann. Math. Ser. B , vol.21 , pp. 323-338
    • Chen, S.1    Yong, J.2
  • 8
    • 0034825435 scopus 로고    scopus 로고
    • Stochastic linear quadratic optimal control problems
    • S. CHEN AND J. YONG, Stochastic linear quadratic optimal control problems, Appl. Math. Optim., 43 (2001), pp. 21-45.
    • (2001) Appl. Math. Optim. , vol.43 , pp. 21-45
    • Chen, S.1    Yong, J.2
  • 9
    • 0020173111 scopus 로고
    • Nonexistence and nonuniqueness of open-loop equilibrium in linear-quadratic differential games
    • T. EISELE, Nonexistence and nonuniqueness of open-loop equilibrium in linear-quadratic differential games, J. Optim. Theory Appl., 37 (1982), pp. 443-468.
    • (1982) J. Optim. Theory Appl. , vol.37 , pp. 443-468
    • Eisele, T.1
  • 10
    • 0002638071 scopus 로고
    • The existence of value in differential games
    • R. J. ELLIOT AND N. J. KALTON, The existence of value in differential games, Mem. Amer. Math. Soc., 126 (1972).
    • (1972) Mem. Amer. Math. Soc. , vol.126
    • Elliot, R.J.1    Kalton, N.J.2
  • 11
    • 0000097584 scopus 로고
    • On the existence of value functions of two-player, zero-sum stochastic differential games
    • W. H. FLEMING AND P. E. SOUGANIDIS, On the existence of value functions of two-player, zero-sum stochastic differential games, Indiana Univ. Math. J., 38 (1989), pp. 293-314.
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 293-314
    • Fleming, W.H.1    Souganidis, P.E.2
  • 13
    • 0039930261 scopus 로고
    • Stochastic differential games
    • A. FRIEDMAN, Stochastic differential games, J. Differential Equations, 11 (1972), pp. 79-108.
    • (1972) J. Differential Equations , vol.11 , pp. 79-108
    • Friedman, A.1
  • 14
    • 0033482670 scopus 로고    scopus 로고
    • Nonzero sum linear-quadratic stochastic differential games and backward-forward equations
    • S. HAMADENE, Nonzero sum linear-quadratic stochastic differential games and backward-forward equations, Stochastic Anal. Appl., 17 (1999), pp. 117-130.
    • (1999) Stochastic Anal. Appl. , vol.17 , pp. 117-130
    • Hamadene, S.1
  • 15
    • 0039662153 scopus 로고
    • Backward equations, stochastic control and zero-sum stochastic differential games
    • S. HAMADENE AND J.-P. LEPELTIER, Backward equations, stochastic control and zero-sum stochastic differential games, Stochastics Stochastics Rep., 54 (1995), pp. 221-231.
    • (1995) Stochastics Stochastics Rep. , vol.54 , pp. 221-231
    • Hamadene, S.1    Lepeltier, J.-P.2
  • 16
    • 0000250431 scopus 로고
    • N-person differential games governed by semilinear stochastic evolution systems
    • Y. Hu, N-person differential games governed by semilinear stochastic evolution systems, Appl. Math. Optim., 24 (1991), pp. 257-271.
    • (1991) Appl. Math. Optim. , vol.24 , pp. 257-271
    • Hu, Y.1
  • 17
    • 0016884705 scopus 로고
    • Linear quadratic differential games in a Hubert space
    • A. ICHIKAWA, Linear quadratic differential games in a Hubert space, SIAM J. Control Optim., 14 (1976), pp. 120-136.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 120-136
    • Ichikawa, A.1
  • 19
    • 0000011589 scopus 로고
    • Contributions to the theory of optimal control
    • R. E. KALMAN, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana, 5 (1960), pp. 102-119.
    • (1960) Bol. Soc. Mat. Mexicana , vol.5 , pp. 102-119
    • Kalman, R.E.1
  • 20
    • 0043156616 scopus 로고
    • Stabilization of systems in which noise is dependent on the value of the control signal
    • N. N. KRASOVSKII, Stabilization of systems in which noise is dependent on the value of the control signal, Eng. Cybern. (USSR), 3 (1965), pp. 94-102.
    • (1965) Eng. Cybern. (USSR) , vol.3 , pp. 94-102
    • Krasovskii, N.N.1
  • 22
    • 0043156615 scopus 로고
    • N-person differential games governed by infinite dimensional systems
    • X. Li, N-person differential games governed by infinite dimensional systems, J. Optim. Theory Appl., 50 (1986), pp. 431-450.
    • (1986) J. Optim. Theory Appl. , vol.50 , pp. 431-450
    • Li, X.1
  • 25
    • 0015203973 scopus 로고
    • Optimal stochastic control of linear systems with state- and control-dependent disturbances
    • P. J. MCLANE, Optimal stochastic control of linear systems with state- and control-dependent disturbances, IEEE Trans. Automat. Control, 16 (1971), pp. 793-798.
    • (1971) IEEE Trans. Automat. Control , vol.16 , pp. 793-798
    • McLane, P.J.1
  • 26
    • 0007229266 scopus 로고
    • A differential game with multi-level of hierarchy
    • L. PAN AND J. YONG, A differential game with multi-level of hierarchy, J. Math. Anal. Appl., 161 (1991), pp. 522-544.
    • (1991) J. Math. Anal. Appl. , vol.161 , pp. 522-544
    • Pan, L.1    Yong, J.2
  • 27
    • 0025262967 scopus 로고
    • Adapted solutions of backward stochastic equations
    • E. PARDOUX AND S. PENG, Adapted solutions of backward stochastic equations, Systems Control Lett., 14 (1990), pp. 55-61.
    • (1990) Systems Control Lett. , vol.14 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 28
    • 0014785373 scopus 로고
    • Existence of optimal open-loop strategies for a class of differential games
    • W. E. SCHMITENDORF, Existence of optimal open-loop strategies for a class of differential games, J. Optim. Theory Appl., 5 (1970), pp. 363-375.
    • (1970) J. Optim. Theory Appl. , vol.5 , pp. 363-375
    • Schmitendorf, W.E.1
  • 29
    • 0000551771 scopus 로고
    • On the existence of Nash equilibrium points in N-person nonzero sum stochastic differential games
    • K. UCHIDA, On the existence of Nash equilibrium points in N-person nonzero sum stochastic differential games, SIAM J. Control Optim., 16 (1978), pp. 142-149.
    • (1978) SIAM J. Control Optim. , vol.16 , pp. 142-149
    • Uchida, K.1
  • 30
    • 0016950494 scopus 로고
    • N-player stochastic differential games
    • P. VARAIYA, N-player stochastic differential games, SIAM J. Control Optim., 14 (1976), pp. 538-545.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 538-545
    • Varaiya, P.1
  • 31
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • W. M. WONHAM, On a matrix Riccati equation of stochastic control, SIAM J. Control, 6 (1968), pp. 681-697.
    • (1968) SIAM J. Control , vol.6 , pp. 681-697
    • Wonham, W.M.1
  • 32
    • 0032794959 scopus 로고    scopus 로고
    • Linear forward-backward stochastic differential equations
    • J. YONG, Linear forward-backward stochastic differential equations, Appl. Math. Optim., 39 (1999), pp. 93-119.
    • (1999) Appl. Math. Optim. , vol.39 , pp. 93-119
    • Yong, J.1
  • 33
    • 0043156614 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equation - A useful tool for mathematical finance and other related fields
    • to appear
    • J. YONG, Forward-backward stochastic differential equation - a useful tool for mathematical finance and other related fields, Survey Industry Math., to appear.
    • Survey Industry Math.
    • Yong, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.