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Volumn 2, Issue 1, 2005, Pages 506-549

On some recent aspects of stochastic control and their applications

(1)  Pham, Huyén a  

a CNRS   (France)

Author keywords

Backward stochastic differential equations; Controlled diffusions; Dynamic programming; Finance; Maximum principle; Viscosity solutions

Indexed keywords


EID: 33845734948     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/154957805100000195     Document Type: Article
Times cited : (68)

References (93)
  • 1
    • 84856568426 scopus 로고
    • Analyse de l'algorithme multigrille FMGH de résolution d'équations d'Hamilton-Jacobi-Bellman
    • Lect. Notes in Contr. and Inf. Sciences,Springer-Verlag
    • Akian M. (1990) : "Analyse de l'algorithme multigrille FMGH de résolution d'équations d'Hamilton-Jacobi-Bellman", Analysis and Optimization of systems, Lect. Notes in Contr. and Inf. Sciences, 144, Springer-Verlag, pp. 113-122.
    • (1990) Analysis and Optimization of systems, , vol.144 , pp. 113-122
    • Akian, M.1
  • 2
    • 0000580597 scopus 로고
    • Backward-forward stochastic differential equations
    • Antonelli F. (1993) : "Backward-forward stochastic differential equations", Annals of Appl. Prob., 3, 777-793.
    • (1993) Annals of Appl. Prob. , vol.3 , pp. 777-793
    • Antonelli, F.1
  • 4
    • 0037843726 scopus 로고    scopus 로고
    • Error analysis of the optimal quantization algorithm for obstacle problems
    • Bally V. and G. Pagès (2003) : "Error analysis of the optimal quantization algorithm for obstacle problems", Stochastic Processes and their Applications, 106, 1-40.
    • (2003) Stochastic Processes, and their Applications , vol.106 , pp. 1-40
    • Bally, V.1    Pagès, G.2
  • 5
    • 0024767145 scopus 로고
    • The partially obsered stochastic minimum principle
    • Baras J., Elliott R., and M. Kohlmann (1989) : "The partially obsered stochastic minimum principle", SIAM J. Cont. Optim., 27, 1279-1292.
    • (1989) SIAM J. Cont. Optim. , vol.27 , pp. 1279-1292
    • Baras, J.1    Elliott, R.2    Kohlmann, M.3
  • 6
    • 25444517488 scopus 로고    scopus 로고
    • Error bounds for monotone approximations schemes for Hamilton-Jacobi-Bellman equations
    • to appear in
    • Barles G., and E. Jakobsen (2004) : "Error bounds for monotone approximations schemes for Hamilton-Jacobi-Bellman equations", to appear in SIAM J. Num. Anal.
    • (2004) SIAM J. Num. Anal.
    • Barles, G.1    Jakobsen, E.2
  • 7
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully non linear second-order equations
    • Barles G., and P. Souganidis (1991) : : "Convergence of approximation schemes for fully non linear second-order equations", Asymptotics Analysis, 4, pp.271-283.
    • (1991) Asymptotics Analysis , vol.4 , pp. 271-283
    • Barles, G.1    Souganidis, P.2
  • 8
    • 85012688561 scopus 로고
    • Dynamic programming
    • Princeton university press
    • Bellman R. (1957) : Dynamic programming, Princeton university press.
    • (1957)
    • Bellman, R.1
  • 9
    • 3943081474 scopus 로고
    • Contrôle impulsionnel et inéquations variationnelles, Dunod
    • Bensoussan A., and J.L. Lions (1982) : Contrôle impulsionnel et inéquations variationnelles, Dunod.
    • (1982)
    • Bensoussan, A.1    Lions, J.L.2
  • 10
    • 0003644258 scopus 로고
    • Stochastic control of partially observable systems
    • Cambridge University Press
    • Bensoussan A. (1992) : Stochastic control of partially observable systems, Cambridge University Press.
    • (1992)
    • Bensoussan, A.1
  • 11
    • 84972565055 scopus 로고
    • An ergodic control problem arising from the principal eigenfunction of an elliptic operator
    • Bensoussan A., and H. Nagai (1991) : "An ergodic control problem arising from the principal eigenfunction of an elliptic operator", J. Math. Soc. Japan, 43, 49-65.
    • (1991) J. Math. Soc. Japan , vol.43 , pp. 49-65
    • Bensoussan, A.1    Nagai, H.2
  • 12
    • 0033130828 scopus 로고    scopus 로고
    • Risk-sensitive dynamic asset management
    • MR1675114
    • Bielecki T., and S. Pliska (1999) : "Risk-sensitive dynamic asset management", Applied Math. Optim., 39, 337-360. MR1675114
    • (1999) Applied Math. Optim. , vol.39 , pp. 337-360
    • Bielecki, T.1    Pliska, S.2
  • 13
    • 14544300310 scopus 로고    scopus 로고
    • Optimal investment, and consumption when time-horizon is uncertain
    • Preprint.
    • Blanchet-Scalliet C., El Karoui N., Jeanblanc M., and L. Martellini (2002) : "Optimal investment, and consumption when time-horizon is uncertain", Preprint.
    • (2002)
    • Blanchet-Scalliet, C.1    El Karoui, N.2    Jeanblanc, M.3    Martellini, L.4
  • 14
    • 1842587080 scopus 로고    scopus 로고
    • Mean-variance hedging, and stochastic control : beyond the Brownian setting
    • Bobrovnytska O., and M. Schweizer (2004) : "Mean-variance hedging, and stochastic control : beyond the Brownian setting", IEE Trans. on Aut. Cont., 49, 1-14.
    • (2004) IEE Trans. on Aut. Cont. , vol.49 , pp. 1-14
    • Bobrovnytska, O.1    Schweizer, M.2
  • 15
    • 0003325079 scopus 로고
    • Optimal control of diffusion processes
    • MR1005532
    • Borkar V. (1989) : Optimal control of diffusion processes, Pitman Research Notes in Math., 203. MR1005532
    • (1989) Pitman Research Notes in Math. , pp. 203
    • Borkar, V.1
  • 16
    • 51549090039 scopus 로고    scopus 로고
    • Controlled diffusion processes
    • Borkar V. (2005) : "Controlled diffusion processes", Probability surveys, 2, 213-244.
    • (2005) Probability surveys , vol.2 , pp. 213-244
    • Borkar, V.1
  • 17
    • 21144436642 scopus 로고    scopus 로고
    • Wealth-path dependent utility maximization in incomplete markets
    • Bouchard B., and H. Pham (2004) : "Wealth-path dependent utility maximization in incomplete markets", Finance, and Stochastics, 8, 579-603.
    • (2004) Finance, and Stochastics , vol.8 , pp. 579-603
    • Bouchard, B.1    Pham, H.2
  • 18
    • 2342427092 scopus 로고    scopus 로고
    • Discrete time approximation, and Monte Carlo simulation of backward stochastic differential equations
    • Bouchard B., and N. Touzi (2004) : "Discrete time approximation, and Monte Carlo simulation of backward stochastic differential equations", Stochastic Processes, and their Applications, 111, 175-206.
    • (2004) Stochastic Processes, and their Applications , vol.111 , pp. 175-206
    • Bouchard, B.1    Touzi, N.2
  • 19
    • 0028467079 scopus 로고
    • Optimal switching in an economic activity under uncertainty
    • Brekke K., and B. Oksendal (1994) : "Optimal switching in an economic activity under uncertainty", SIAM J. Cont. Optim., 32, 1021-1036.
    • (1994) SIAM J. Cont. Optim. , vol.32 , pp. 1021-1036
    • Brekke, K.1    Oksendal, B.2
  • 20
    • 0040249268 scopus 로고    scopus 로고
    • Optimal replication of contingent claims under portfolio constraints
    • Broadie M., Cvitanic J., and M. Soner (1998) : "Optimal replication of contingent claims under portfolio constraints", Review of Fin. Studies, 11, 59-79.
    • (1998) Review of Fin. Studies , vol.11 , pp. 59-79
    • Broadie, M.1    Cvitanic, J.2    Soner, M.3
  • 21
    • 49749133784 scopus 로고    scopus 로고
    • Optimal multiple stopping, and the valuation of swing options
    • to appear in
    • Carmona R., and N. Touzi (2004) : "Optimal multiple stopping, and the valuation of swing options", to appear in Mathematical Finance.
    • (2004) Mathematical Finance
    • Carmona, R.1    Touzi, N.2
  • 22
  • 23
    • 84967708673 scopus 로고
    • User's Guide to Viscosity Solutions of Second Order Partial Differential Equations
    • Crandall M., Ishii. H, and P.L. Lions (1992) : "User's Guide to Viscosity Solutions of Second Order Partial Differential Equations", Bull. Amer. Math. Soc., 27, 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 24
    • 0033235821 scopus 로고    scopus 로고
    • Superreplication in stochastic volatility models under portfolio constraints
    • MR1724796
    • Cvitanic J., Pham H., and N. Touzi (1999a) : "Superreplication in stochastic volatility models under portfolio constraints", Journal of Appplied Probability, 36, 523-545. MR1724796
    • (1999) Journal of Appplied Probability , vol.36 , pp. 523-545
    • Cvitanic, J.1    Pham, H.2    Touzi, N.3
  • 25
    • 0002241143 scopus 로고    scopus 로고
    • A closed form solution for the super-replication problem under transaction costs
    • Cvitanic J., Pham H., and N. Touzi (1999b) : "A closed form solution for the super-replication problem under transaction costs", Finance, and Stochastics, 3, 35-54.
    • (1999) Finance, and Stochastics , vol.3 , pp. 35-54
    • Cvitanic, J.1    Pham, H.2    Touzi, N.3
  • 26
    • 0000649234 scopus 로고
    • Dynamic programming conditions for partially observable systems
    • Davis M., and P. Varaiya (1973) : "Dynamic programming conditions for partially observable systems", SIAM J. Cont., 11, 226-261.
    • (1973) SIAM J. Cont. , vol.11 , pp. 226-261
    • Davis, M.1    Varaiya, P.2
  • 27
    • 0036233502 scopus 로고    scopus 로고
    • On the existence, and uniqueness of solutions to FBSDEs in a non-degenerate case
    • Delarue, F. (2002) : "On the existence, and uniqueness of solutions to FBSDEs in a non-degenerate case". Stoch. Process. Appl., 99, 209-286.
    • (2002) Stoch. Process. Appl. , vol.99 , pp. 209-286
    • Delarue, F.1
  • 28
    • 34248509236 scopus 로고    scopus 로고
    • A forward-backward stochastic algorithm for quasi-linear PDEs
    • to appear in
    • Delarue F., and S. Menozzi (2004) : "A forward-backward stochastic algorithm for quasi-linear PDEs", to appear in Annals of Applied Probability.
    • (2004) Annals of Applied Probability
    • Delarue, F.1    Menozzi, S.2
  • 29
    • 0030520557 scopus 로고    scopus 로고
    • Numerical methods for forwardbackward stochastic differential equations
    • Douglas J., Ma J., and P. Protter (1996) : "Numerical methods for forwardbackward stochastic differential equations", Annals of Applied Probability, 6, 940-968.
    • (1996) Annals of Applied Probability , vol.6 , pp. 940-968
    • Douglas, J.1    Ma, J.2    Protter, P.3
  • 30
    • 0035592033 scopus 로고    scopus 로고
    • A model for investment decisions with switching costs
    • Duckworth K., and M. Zervos (2001) : "A model for investment decisions with switching costs", Annals of Applied Probability, 11, 239-250.
    • (2001) Annals of Applied Probability , vol.11 , pp. 239-250
    • Duckworth, K.1    Zervos, M.2
  • 31
    • 0001866003 scopus 로고
    • Les Aspects Probabilistes du Contrôle Stochastique
    • Springer Verlag
    • El Karoui N. (1981) : Les Aspects Probabilistes du Contrôle Stochastique, Lect. Notes in Math., 816, Springer Verlag.
    • (1981) Lect. Notes in Math. , vol.816
    • El Karoui, N.1
  • 32
    • 0002234857 scopus 로고    scopus 로고
    • Backward stochastic differential equations
    • editors, Pitman research notes in mathematics series
    • El Karoui N., and L. Mazliak (editors) (1997) : Backward stochastic differential equations, Pitman research notes in mathematics series.
    • (1997)
    • El Karoui, N.1    Mazliak, L.2
  • 33
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equations in finance
    • MR1434407
    • El Karoui N., S. Peng, and M.C. Quenez (1997) : "Backward stochastic differential equations in finance", Mathematical Finance, 7, 1-71. MR1434407
    • (1997) Mathematical Finance , vol.7 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 34
    • 0002335001 scopus 로고
    • Dynamic programming, and pricing contingent claims in incomplete markets
    • MR1311659
    • El Karoui N., and M.C. Quenez (1995) : "Dynamic programming, and pricing contingent claims in incomplete markets", SIAM J. Cont. Optim., 33, 29-
    • (1995) SIAM J. Cont. Optim. , vol.33 , pp. 29-66
    • El Karoui, N.1    Quenez, M.C.2
  • 35
    • 0000384159 scopus 로고
    • Numerical methods for an optimal Investment-Consumption Model
    • Fitzpatrick B., and W. Fleming (1991) : "Numerical methods for an optimal Investment-Consumption Model", Mathematics of Operation Research, 16, pp.823-841.
    • (1991) Mathematics of Operation Research , vol.16 , pp. 823-841
    • Fitzpatrick, B.1    Fleming, W.2
  • 36
    • 0042404654 scopus 로고
    • Optimal control of partially observable systems
    • Fleming W. (1968) : "Optimal control of partially observable systems", SIAM J. Cont. Optim., 6, 194-214.
    • (1968) SIAM J. Cont. Optim. , vol.6 , pp. 194-214
    • Fleming, W.1
  • 37
    • 1842450989 scopus 로고    scopus 로고
    • An optimal consumption model with stochastic volatility
    • Fleming, W., and D. Hernandez-Hernandez (2003) : "An optimal consumption model with stochastic volatility", Finance Stoch., 7, 245-262.
    • (2003) Finance Stoch. , vol.7 , pp. 245-262
    • Fleming, W.1    Hernandez-Hernandez, D.2
  • 38
    • 0001234347 scopus 로고
    • Risk-sensitive control on an infinite horizon
    • Fleming W., and W. McEneaney (1995) : "Risk-sensitive control on an infinite horizon", SIAM J. Cont., and Optim., 33, 1881-1915.
    • (1995) SIAM J. Cont., and Optim. , vol.33 , pp. 1881-1915
    • Fleming, W.1    McEneaney, W.2
  • 39
    • 0003923089 scopus 로고
    • Deterministic, and stochastic optimal control
    • Springer Verlag
    • Fleming W., and R. Rishel (1975) : Deterministic, and stochastic optimal control, Springer Verlag.
    • (1975)
    • Fleming, W.1    Rishel, R.2
  • 40
    • 0034392970 scopus 로고    scopus 로고
    • Risk sensitive control, and an optimal investment model
    • MR1802598
    • Fleming W., and S. Sheu (2000) : "Risk sensitive control, and an optimal investment model", Math. Finance, 10, 197-213. MR1802598
    • (2000) Math. Finance , vol.10 , pp. 197-213
    • Fleming, W.1    Sheu, S.2
  • 41
    • 0003423896 scopus 로고
    • Controlled Markov processes, and viscosity solutions
    • Springer Verlag
    • Fleming W., and M. Soner (1993) : Controlled Markov processes, and viscosity solutions, Springer Verlag.
    • (1993)
    • Fleming, W.1    Soner, M.2
  • 42
    • 84969156046 scopus 로고    scopus 로고
    • On a class of stochastic optimal control problems related to BSDEs with quadratic growth
    • Preprint
    • Fuhrman M., Hu Y., and G. Tessitore (2005) : "On a class of stochastic optimal control problems related to BSDEs with quadratic growth", Preprint.
    • (2005)
    • Fuhrman, M.1    Hu, Y.2    Tessitore, G.3
  • 43
    • 84890602969 scopus 로고    scopus 로고
    • A regression-based Monte- Carlo method for backward stochastic differential equations
    • to appear in
    • Gobet E., Lemor J.P., and X. Warin (2004) : "A regression-based Monte- Carlo method for backward stochastic differential equations", to appear in Annals of Applied Probability.
    • (2004) Annals of Applied Probability.
    • Gobet, E.1    Lemor, J.P.2    Warin, X.3
  • 44
    • 17444364489 scopus 로고    scopus 로고
    • Robust utility maximization for complete, and incomplete market models
    • Gundel A. (2004) : "Robust utility maximization for complete, and incomplete market models", Finance, and Stochastics, 9, 151-176.
    • (2004) Finance, and Stochastics , vol.9 , pp. 151-176
    • Gundel, A.1
  • 45
    • 0035597611 scopus 로고    scopus 로고
    • An explicit solution to an optimal stopping problem with regime switching
    • Guo X. (2001) : "An explicit solution to an optimal stopping problem with regime switching", Journal of Applied Probability, 38, 464-481.
    • (2001) Journal of Applied Probability , vol.38 , pp. 464-481
    • Guo, X.1
  • 46
    • 16244417484 scopus 로고    scopus 로고
    • Optimal partially reversible investment with entry decision, and general production function
    • MR2132595
    • Guo X., and H. Pham (2005) : "Optimal partially reversible investment with entry decision, and general production function", Stoc. Proc. Appli., 115, 705-736. MR2132595
    • (2005) Stoc. Proc. Appli. , vol.115 , pp. 705-736
    • Guo, X.1    Pham, H.2
  • 47
    • 33846886446 scopus 로고    scopus 로고
    • Solving a large deviations control problem with a nonlinear factor model
    • Preprint
    • Hata H., and J. Sekine (2005) : "Solving a large deviations control problem with a nonlinear factor model", Preprint.
    • (2005)
    • Hata, H.1    Sekine, J.2
  • 48
    • 51249168165 scopus 로고
    • Solution of forward-backward stochastic differential equations
    • Hu Y., and S. Peng (1995) : "Solution of forward-backward stochastic differential equations", Prob. Theo. Rel. Fields, 103, 273-283.
    • (1995) Prob. Theo. Rel. Fields , vol.103 , pp. 273-283
    • Hu, Y.1    Peng, S.2
  • 49
    • 84956277096 scopus 로고
    • Optimization of the ow of dividends
    • Jeanblanc M., and A. Shiryaev (1995) : "Optimization of the ow of dividends", Russian Math Surveys, 50, 257-277.
    • (1995) Russian Math Surveys , vol.50 , pp. 257-277
    • Jeanblanc, M.1    Shiryaev, A.2
  • 50
    • 24144452773 scopus 로고    scopus 로고
    • A geometric approach to portfolio optimization in models with transaction costs
    • Kabanov, Yu., and C. Kluppelberg (2004) : "A geometric approach to portfolio optimization in models with transaction costs", Finance, and Stochastics, 8, 207-227.
    • (2004) Finance, and Stochastics , vol.8 , pp. 207-227
    • Kabanov, Y.U.1    Kluppelberg, C.2
  • 51
    • 0019214633 scopus 로고
    • On a stochastic representation for the principal eigenvalue of a second order differential equation
    • Karatzas I. (1980) : "On a stochastic representation for the principal eigenvalue of a second order differential equation", Stochastics, and Stochastics Reports, 3, 305-321.
    • (1980) Stochastics, and Stochastics Reports , vol.3 , pp. 305-321
    • Karatzas, I.1
  • 52
    • 0034345576 scopus 로고    scopus 로고
    • Backward stochastic differential equations, and partial differential equations with quadratic growth
    • Kobylanski M. (2000) : "Backward stochastic differential equations, and partial differential equations with quadratic growth", Annals of Probability, 28, 558-602.
    • (2000) Annals of Probability , vol.28 , pp. 558-602
    • Kobylanski, M.1
  • 53
    • 0036144125 scopus 로고    scopus 로고
    • Global adapted solution of onedimensional backward stochastic differential Riccati equations, with application to the mean-variance hedging
    • Kohlmann M., and S. Tang (2002) : "Global adapted solution of onedimensional backward stochastic differential Riccati equations, with application to the mean-variance hedging", Stochastic Process. Appl., 97, 255-288.
    • (2002) Stochastic Process. Appl. , vol.97 , pp. 255-288
    • Kohlmann, M.1    Tang, S.2
  • 54
    • 0033719602 scopus 로고    scopus 로고
    • Relationship between backward stochastic differential equations, and stochastic controls : a linear-quadratic approach
    • Kohlmann M., and X.Y. Zhou (2000) : "Relationship between backward stochastic differential equations, and stochastic controls : a linear-quadratic approach", SIAM Journal on Control, and Optimization, 38, 1392-1407.
    • (2000) SIAM Journal on Control, and Optimization , vol.38 , pp. 1392-1407
    • Kohlmann, M.1    Zhou, X.Y.2
  • 55
    • 0012273782 scopus 로고    scopus 로고
    • Portfolio optimization with strictly positive transaction costs, and impulse control
    • Korn R. (1998) : "Portfolio optimization with strictly positive transaction costs, and impulse control", Finance, and Stochastics, 2, 85-114.
    • (1998) Finance, and Stochastics , vol.2 , pp. 85-114
    • Korn, R.1
  • 56
    • 0004275483 scopus 로고
    • Controlled Diffusion Processes
    • Springer Verlag
    • Krylov N. (1980) : Controlled Diffusion Processes, Springer Verlag.
    • (1980)
    • Krylov, N.1
  • 57
    • 0034384390 scopus 로고    scopus 로고
    • On the rate of convergence of finite difference approximations for Bellman's equations with variable coefficients
    • Krylov N. (2000) : "On the rate of convergence of finite difference approximations for Bellman's equations with variable coefficients", Probab. Theory Relat. Fields, 117, 1-16.
    • (2000) Probab. Theory Relat. Fields , vol.117 , pp. 1-16
    • Krylov, N.1
  • 58
    • 0003861445 scopus 로고
    • Approximation, and weak convergence methods for random processes, with applications to stochastic systems theory
    • MIT Press Series in Signal Processing, Optimization,, and Control, 6, MIT Press, Cambridge, MA 1984
    • Kushner H.J. (1977) : "Approximation, and weak convergence methods for random processes, with applications to stochastic systems theory", MIT Press Series in Signal Processing, Optimization,, and Control, 6, MIT Press, Cambridge, MA, 1984, 269 pp.
    • (1977) , pp. 269
    • Kushner, H.J.1
  • 59
    • 0003924011 scopus 로고    scopus 로고
    • Numerical methods for stochastic control problems in continuous time
    • 2nd edition, Applications of Mathematics, 24, Stochastic Modelling, and Applied Probability, Springer-Verlag, New York
    • Kushner H.J., and P. Dupuis (2001) : Numerical methods for stochastic control problems in continuous time, 2nd edition, Applications of Mathematics, 24, Stochastic Modelling, and Applied Probability, Springer-Verlag, New York, 475 pp.
    • (2001) , pp. 475
    • Kushner, H.J.1    Dupuis, P.2
  • 60
    • 0003690985 scopus 로고
    • Linear, and quasilinear equations of parabolic type
    • American Mathematical Society, Providence
    • Ladyzhenskaya O., Solonnikov V., and N. Uralseva (1968) : Linear, and quasilinear equations of parabolic type, American Mathematical Society, Providence.
    • (1968)
    • Ladyzhenskaya, O.1    Solonnikov, V.2    Uralseva, N.3
  • 61
    • 84947513018 scopus 로고
    • Optimal control of diffusion processes, and Hamilton- Jacobi-Bellman equations"
    • 1229-1276
    • Lions P.L. (1983) : "Optimal control of diffusion processes, and Hamilton- Jacobi-Bellman equations"", Comm. P.D.E, 8, Part I, 1101-1134, Part II, 1229-1276
    • (1983) Comm. P.D.E , vol.8 , pp. 1101-1134
    • Lions, P.L.1
  • 62
    • 34250087346 scopus 로고
    • Viscosity solutions, and optimal stochastic control in infinite dimension
    • Lions P.L. (1988) : "Viscosity solutions, and optimal stochastic control in infinite dimension", Part I Acta Math., 161, 243-278.
    • (1988) Part I Acta Math. , vol.161 , pp. 243-278
    • Lions, P.L.1
  • 64
    • 0036101915 scopus 로고    scopus 로고
    • Numerical method for backward stochastic differential equations
    • Ma J., Protter P., San Martin J., and S. Torres (2002) : "Numerical method for backward stochastic differential equations", Ann. Appl. Prob., 12, 302- 316.
    • (2002) Ann. Appl. Prob. , vol.12
    • Ma, J.1    Protter, P.2    San Martin, J.3    Torres, S.4
  • 65
    • 0344891803 scopus 로고
    • Solving forward-backward stochastic differential equations explicitly : a four step scheme
    • Ma J., Protter P., and J. Yong (1994) : "Solving forward-backward stochastic differential equations explicitly : a four step scheme", Prob. Theo. Rel. Fields, 98, 339-359.
    • (1994) Prob. Theo. Rel. Fields , vol.98 , pp. 339-359
    • Ma, J.1    Protter, P.2    Yong, J.3
  • 66
    • 0004254055 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations, and their applications
    • Ma J., and J. Yong (2000) : Forward-backward stochastic differential equations, and their applications, Lect. Notes in Math., 1702.
    • (2000) Lect. Notes in Math. , pp. 1702
    • Ma, J.1    Yong, J.2
  • 67
    • 0242593868 scopus 로고    scopus 로고
    • Backward stochastic PDE, and imperfect hedging
    • Mania M., and R. Tevzadze (2003) : "Backward stochastic PDE, and imperfect hedging", Int. J. Theo. App. Fin., 6, 663-692.
    • (2003) Int. J. Theo. App. Fin. , vol.6 , pp. 663-692
    • Mania, M.1    Tevzadze, R.2
  • 68
    • 33746008117 scopus 로고
    • Lectures on Stochastic Control Theory
    • ISI Lect. Notes, 9, Kaigai Publ. Osaka
    • Nisio M. (1981) : Lectures on Stochastic Control Theory, ISI Lect. Notes, 9, Kaigai Publ. Osaka.
    • (1981)
    • Nisio, M.1
  • 69
    • 0036929730 scopus 로고    scopus 로고
    • Optimal consumption, and portfolio with both fixed, and proportional transaction costs
    • Oksendal B., and A. Sulem (2002) : "Optimal consumption, and portfolio with both fixed, and proportional transaction costs", SIAM J. Cont. Optim., 40, 1765-1790.
    • (2002) SIAM J. Cont. Optim. , vol.40 , pp. 1765-1790
    • Oksendal, B.1    Sulem, A.2
  • 70
    • 4344665765 scopus 로고    scopus 로고
    • Applied stochastic control of jump diffusion
    • Springer Verlag. MR2109687
    • Oksendal B., and A. Sulem (2004) : Applied stochastic control of jump diffusion, Springer Verlag. MR2109687
    • (2004)
    • Oksendal, B.1    Sulem, A.2
  • 71
    • 37849009529 scopus 로고    scopus 로고
    • An optimal Markovian quantization algorithm for multi-dimensional stochastic control problems
    • Pagès G., Pham H., and J. Printems (2004a) : "An optimal Markovian quantization algorithm for multi-dimensional stochastic control problems", Stochastics, and Dynamics, 4, 501-545.
    • (2004) Stochastics, and Dynamics , vol.4 , pp. 501-545
    • Pagès, G.1    Pham, H.2    Printems, J.3
  • 72
    • 33645685536 scopus 로고    scopus 로고
    • Optimal quantization methods, and applications to numerical problems in finance
    • in Handbook of computational, and numerical methods in finance, ed. S. Rachev, Birkhäuser. MR2083048
    • Pagès G., Pham H., and J. Printems (2004b) : "Optimal quantization methods, and applications to numerical problems in finance", in Handbook of computational, and numerical methods in finance, ed. S. Rachev, Birkhäuser. MR2083048
    • (2004)
    • Pagès, G.1    Pham, H.2    Printems, J.3
  • 73
    • 0025262967 scopus 로고
    • Adapted solutions of a backward stochastic differential equation
    • Pardoux E., and S. Peng (1990) : "Adapted solutions of a backward stochastic differential equation", Systems, and Control Letters, 14, 55-61.
    • (1990) Systems, and Control Letters , vol.14 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 74
    • 0033463544 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations, and quasilinear parabolic pdes
    • Pardoux E., and S. Tang (1999) : "Forward-backward stochastic differential equations, and quasilinear parabolic pdes ", Prob. Theo. Rel. Fields., 114, 123-150.
    • (1999) Prob. Theo. Rel. Fields. , vol.114 , pp. 123-150
    • Pardoux, E.1    Tang, S.2
  • 75
    • 0025462369 scopus 로고
    • A general stochastic maximum principle for optimal control diffusions
    • Peng S. (1990) : "A general stochastic maximum principle for optimal control diffusions", SIAM J. Cont. Optim., 28, 966-979.
    • (1990) SIAM J. Cont. Optim. , vol.28 , pp. 966-979
    • Peng, S.1
  • 76
    • 1842555622 scopus 로고    scopus 로고
    • On quadratic hedging in continuous time
    • Pham H. (2000) : "On quadratic hedging in continuous time", Math. Meth. Oper. Res., 51, 315-339.
    • (2000) Math. Meth. Oper. Res. , vol.51 , pp. 315-339
    • Pham, H.1
  • 77
    • 0141904066 scopus 로고    scopus 로고
    • Smooth solutions to optimal investment models with stochastic volatilities, and portfolio constraints
    • Pham H. (2002) : "Smooth solutions to optimal investment models with stochastic volatilities, and portfolio constraints", Appl. Math. Optim., 46, 55-78.
    • (2002) Appl. Math. Optim. , vol.46 , pp. 55-78
    • Pham, H.1
  • 78
    • 0037640275 scopus 로고    scopus 로고
    • A large deviations approach to optimal long term investment'
    • Pham H. (2003a) : "A large deviations approach to optimal long term investment'", Finance, and Stochastics, 7, 169-195.
    • (2003) Finance, and Stochastics , vol.7 , pp. 169-195
    • Pham, H.1
  • 79
    • 0038719701 scopus 로고    scopus 로고
    • A risk-sensitive control dual approach to a large deviations control problem
    • Pham H. (2003b) : "A risk-sensitive control dual approach to a large deviations control problem", Systems, and Control Letters, 49, 295-309.
    • (2003) Systems, and Control Letters , vol.49 , pp. 295-309
    • Pham, H.1
  • 80
    • 57649196845 scopus 로고    scopus 로고
    • On the smooth-fit property for one-dimensional optimal switching problem
    • to appear in
    • Pham H. (2005a) : "On the smooth-fit property for one-dimensional optimal switching problem", to appear in Séminaire de Probabilités, Vol. XL.
    • (2005) Séminaire de Probabilités , vol.40
    • Pham, H.1
  • 81
    • 70450189702 scopus 로고    scopus 로고
    • Optimisation et contrôle stochastique appliqués à la finance
    • to appear, Series Mathématiques et Applications, Springer Verlag
    • Pham H. (2005b) : Optimisation et contrôle stochastique appliqués à la finance, to appear, Series Mathématiques et Applications, Springer Verlag.
    • (2005)
    • Pham, H.1
  • 82
    • 84890597539 scopus 로고    scopus 로고
    • Optimal investment for robust utility functionals in complete markets
    • to appear in
    • Schied A. (2003) : "Optimal investment for robust utility functionals in complete markets", to appear in Mathematics of Operations Research.
    • (2003) Mathematics of Operations Research
    • Schied, A.1
  • 83
    • 0012743619 scopus 로고    scopus 로고
    • A guided tour through quadratic hedging approaches
    • in Option pricing, Interest rates, and risk management, J. Cvitanic, E. Jouini,, and m. Musiela eds., Cambridge Univ. Press
    • Schweizer M. (2001) : "A guided tour through quadratic hedging approaches", in Option pricing, Interest rates, and risk management, J. Cvitanic, E. Jouini,, and m. Musiela eds., Cambridge Univ. Press.
    • (2001)
    • Schweizer, M.1
  • 84
    • 0000557964 scopus 로고
    • Optimal investment, and consumption with transaction costs
    • Shreve S., and M. Soner (1994) : "Optimal investment, and consumption with transaction costs", Annals of Applied Probability, 4, 609-692.
    • (1994) Annals of Applied Probability , vol.4 , pp. 609-692
    • Shreve, S.1    Soner, M.2
  • 86
    • 0037249034 scopus 로고    scopus 로고
    • Stochastic target problems, dynamic programming, and viscosity solutions
    • Soner M., and N. Touzi (2002) : "Stochastic target problems, dynamic programming, and viscosity solutions", SIAM Journal on Control, and Optimization, 41, 404-424.
    • (2002) SIAM Journal on Control, and Optimization , vol.41 , pp. 404-424
    • Soner, M.1    Touzi, N.2
  • 87
    • 0012219336 scopus 로고
    • Finite horizon stochastic optimal switching, and impulse controls with a viscosity solution approach
    • MR1306930
    • Tang S., and J. Yong (1993) : "Finite horizon stochastic optimal switching, and impulse controls with a viscosity solution approach", Stoch., and Stoch. Reports, 45, 145-176. MR1306930
    • (1993) Stoch., and Stoch. Reports , vol.45 , pp. 145-176
    • Tang, S.1    Yong, J.2
  • 88
    • 0010966556 scopus 로고
    • Numerical schemes for investment models with singular transactions
    • Tourin A., and T. Zariphopoulou (1994) : "Numerical schemes for investment models with singular transactions", Computational Economics, 7, pp.287-307.
    • (1994) Computational Economics , vol.7 , pp. 287-307
    • Tourin, A.1    Zariphopoulou, T.2
  • 89
    • 0003810314 scopus 로고    scopus 로고
    • Stochastic controls, Hamiltonian systems, and HJB equations
    • Springer Verlag. MR1696772
    • Yong J., and X.Y. Zhou (2000) : Stochastic controls, Hamiltonian systems, and HJB equations, Springer Verlag. MR1696772
    • (2000)
    • Yong, J.1    Zhou, X.Y.2
  • 90
    • 0346853081 scopus 로고
    • Optimal investment-consumption models with constraints
    • Brown University, Phd.
    • Zariphopoulou T. (1988) : Optimal investment-consumption models with constraints, Brown University, Phd.
    • (1988)
    • Zariphopoulou, T.1
  • 91
    • 0010592742 scopus 로고    scopus 로고
    • A solution approach to valuation with unhedgeable risks
    • MR1807876
    • Zariphopoulou T. (2001) : "A solution approach to valuation with unhedgeable risks", Finance, and Stochastics, 5, 61-82. MR1807876
    • (2001) Finance, and Stochastics , vol.5 , pp. 61-82
    • Zariphopoulou, T.1
  • 92
    • 14544284573 scopus 로고    scopus 로고
    • Utility Maximization with a Stochastic Clock, and an Unbounded Random Endowment
    • Zitkovic G. (2005) : "Utility Maximization with a Stochastic Clock, and an Unbounded Random Endowment", Annals of Applied Probability, 15, 748-777.
    • (2005) Annals of Applied Probability , vol.15 , pp. 748-777
    • Zitkovic, G.1
  • 93
    • 0027697778 scopus 로고
    • On the necessary conditions of optimal controls for stochastic partial differential equations
    • Zhou X.Y. (1993) : "On the necessary conditions of optimal controls for stochastic partial differential equations", SIAM J. Cont. Optim., 31, 1462- 1478.
    • (1993) SIAM J. Cont. Optim. , vol.31
    • Zhou, X.Y.1


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