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Volumn 42, Issue 1, 2003, Pages 53-75

General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations

Author keywords

Backward stochastic differential equations; Homomorphism of stochastic flows; Linear quadratic optimal stochastic control; Optimality conditions; Random coefficients; Riccati equation; Stochastic Hamilton flows

Indexed keywords

HAMILTONIANS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; RICCATI EQUATIONS; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING;

EID: 1842532397     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901387550     Document Type: Article
Times cited : (168)

References (24)
  • 1
    • 0000828808 scopus 로고
    • Functional equations in the theory of dynamic programming, positivity and quasi-linearity
    • R. BELLMAN, Functional equations in the theory of dynamic programming, positivity and quasi-linearity, Proc. Natl. Acad. Sci. USA, 41 (1955), pp. 743-746.
    • (1955) Proc. Natl. Acad. Sci. USA , vol.41 , pp. 743-746
    • Bellman, R.1
  • 3
    • 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
  • 4
    • 0007791583 scopus 로고
    • Controle des systems lineares quadratiques: Applications de l'integrale stochastique
    • Séminaire de Probabilités XII, C. Dellacherie, P. A. Meyer, and M. Weil, eds., Springer-Verlag, Berlin
    • J. M. BISMUT, Controle des systems lineares quadratiques: applications de l'integrale stochastique, in Séminaire de Probabilités XII, Lecture Notes in Math. 649, C. Dellacherie, P. A. Meyer, and M. Weil, eds., Springer-Verlag, Berlin, 1978, pp. 180-264.
    • (1978) Lecture Notes in Math. , vol.649 , pp. 180-264
    • Bismut, J.M.1
  • 5
    • 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
  • 6
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic stochastic differential equations in finance
    • N. EL KAROUI, S. PENG, AND M. C. QUENEZ, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), pp. 1-71.
    • (1997) Math. Finance , vol.7 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 7
    • 0007838323 scopus 로고
    • Existence and uniqueness of a solution for stochastic equations with respect to semimartingales
    • L. I. GAL'CHUK, Existence and uniqueness of a solution for stochastic equations with respect to semimartingales, Theory Probab. Appl., 23 (1978), pp. 751-763.
    • (1978) Theory Probab. Appl. , vol.23 , pp. 751-763
    • Gal'chuk, L.I.1
  • 8
    • 0030637337 scopus 로고    scopus 로고
    • Résultats d'existence et d'unicité pour des équations différentielles stochastiques rétrogrades avec des générateurs á croissance quadratique
    • M. KOBYLANSKI, Résultats d'existence et d'unicité pour des équations différentielles stochastiques rétrogrades avec des générateurs á croissance quadratique, C. R. Acad. Sci. Paris Sér I. Math., 324 (1997), pp. 81-86.
    • (1997) C. R. Acad. Sci. Paris Sér I. Math , vol.324 , pp. 81-86
    • Kobylanski, M.1
  • 10
    • 0036144125 scopus 로고    scopus 로고
    • Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging
    • M. KOHLMANN AND S. TANG, Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging, Stochastic Process. Appl., 97 (2002), pp. 255-288.
    • (2002) Stochastic Process. Appl. , vol.97 , pp. 255-288
    • Kohlmann, M.1    Tang, S.2
  • 11
    • 0348220628 scopus 로고    scopus 로고
    • Multidimensional backward stochastic Riccati equations and applications
    • M. KOHLMANN AND S. TANG, Multidimensional backward stochastic Riccati equations and applications, SIAM J. Control Optim., 41 (2003), pp. 1696-1721.
    • (2003) SIAM J. Control Optim. , vol.41 , pp. 1696-1721
    • Kohlmann, M.1    Tang, S.2
  • 12
    • 0347872859 scopus 로고    scopus 로고
    • New developments in backward stochastic Riccati equations and their applications
    • M. Kohlmann and S. Tang, eds., Birkhäuser, Basel
    • M. KOHLMANN AND S. TANG, New developments in backward stochastic Riccati equations and their applications, in Mathematical Finance (Konstanz, 2000), M. Kohlmann and S. Tang, eds., Birkhäuser, Basel, 2001, pp. 194-214.
    • (2001) Mathematical Finance (Konstanz, 2000) , pp. 194-214
    • Kohlmann, M.1    Tang, S.2
  • 13
    • 0031116187 scopus 로고    scopus 로고
    • Backward stochastic differential equations with continuous coefficient
    • J. P. LEPELTIER AND J. SAN MARTIN, Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett., 32 (1997), pp. 425-430.
    • (1997) Statist. Probab. Lett. , vol.32 , pp. 425-430
    • Lepeltier, J.P.1    San Martin, J.2
  • 14
    • 0007745477 scopus 로고    scopus 로고
    • Existence for BSDE with super linear-quadratic coefficient
    • J. P. LEPELTIER AND J. SAN MARTIN, Existence for BSDE with super linear-quadratic coefficient, Stochastics Stochastics Rep., 63 (1998), pp. 227-240.
    • (1998) Stochastics Stochastics Rep , vol.63 , pp. 227-240
    • Lepeltier, J.P.1    San Martin, J.2
  • 16
    • 0025262967 scopus 로고
    • Adapted solution of backward stochastic equation
    • E. PARDOUX AND S. PENG, Adapted solution of backward stochastic equation, Systems Control Lett., 14 (1990), pp. 55-61.
    • (1990) Systems Control Lett. , vol.14 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 17
    • 0000268709 scopus 로고
    • Backward stochastic differential equations and quasi-linear parabolic partial differential equations
    • Stochastic Partial Differential Equations and Their Applications, B. L. Rozovskii and R. S. Sowers, eds., Springer, Berlin, Heidelberg, New York
    • E. PARDOUX AND S. PENG, Backward stochastic differential equations and quasi-linear parabolic partial differential equations, in Stochastic Partial Differential Equations and Their Applications, Lecture Notes in Control and Inform. Sci. 176, B. L. Rozovskii and R. S. Sowers, eds., Springer, Berlin, Heidelberg, New York 1992, pp. 200-217.
    • (1992) Lecture Notes in Control and Inform. Sci. , vol.176 , pp. 200-217
    • Pardoux, E.1    Peng, S.2
  • 18
    • 0026834859 scopus 로고
    • Stochastic Hamilton-Jacobi-Bellman equations
    • S. PENG, Stochastic Hamilton-Jacobi-Bellman equations, SIAM J. Control Optim., 30 (1992), pp. 284-304.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 284-304
    • Peng, S.1
  • 19
    • 0007843755 scopus 로고    scopus 로고
    • Open problems on backward stochastic differential equations
    • S. Chen, et al., eds., Kluwer Academic Publishers, Boston
    • S. PENG, Open problems on backward stochastic differential equations, in Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), S. Chen, et al., eds., Kluwer Academic Publishers, Boston, 1999, pp. 265-273.
    • (1999) Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998) , pp. 265-273
    • Peng, S.1
  • 20
    • 0025462369 scopus 로고
    • A General stochastic maximum principle for optimal control problems
    • S. PENG, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim., 28 (1990), pp. 966-979.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 966-979
    • Peng, S.1
  • 21
    • 0032634560 scopus 로고    scopus 로고
    • Fully coupled forward-backward stochastic differential equations and applications to optimal control
    • S. PENG AND Z. WU, Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., 37 (1999), pp. 825-843.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 825-843
    • Peng, S.1    Wu, Z.2
  • 22
    • 0028500888 scopus 로고
    • Necessary conditions for optimal control of stochastic systems with random jumps
    • S. TANG AND X. LI, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim., 32 (1994), pp. 1447-1475.
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1447-1475
    • Tang, S.1    Li, X.2
  • 23
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.