M. Akian, Analyse de l???algorithme multigrille FMGH de r??solution d?????quations d???Hamilton-Jacobi-Bellman, Lect. Notes in Contr. and Inf. Sciences, vol.144, pp.113-122, 1990.
DOI : 10.1007/BFb0120034

F. Antonelli, Backward-Forward Stochastic Differential Equations, The Annals of Applied Probability, vol.3, issue.3, pp.777-793, 1993.
DOI : 10.1214/aoap/1177005363

P. Artzner, F. Delbaen, J. M. Eber, and D. Heath, Coherent Measures of Risk, Mathematical Finance, vol.9, issue.3, pp.203-228, 1999.
DOI : 10.1111/1467-9965.00068

V. Bally and G. Pagès, Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Processes and their Applications, pp.1-40, 2003.
DOI : 10.1016/S0304-4149(03)00026-7

URL : https://hal.archives-ouvertes.fr/hal-00103987

J. Baras, R. Elliott, and M. Kohlmann, The Partially Observed Stochastic Minimum Principle, SIAM Journal on Control and Optimization, vol.27, issue.6, pp.1279-1292, 1989.
DOI : 10.1137/0327065

G. Barles and E. Jakobsen, Error bounds for monotone approximations schemes for Hamilton-Jacobi-Bellman equations, 2004.

G. Barles and P. Souganidis, Convergence of approximation schemes for fully non linear second-order equations, Asymptotics Analysis, vol.4, pp.271-283, 1991.

R. Bellman, Dynamic programming, 1957.

A. Bensoussan, Stochastic control of partially observable systems, 1992.
DOI : 10.1017/CBO9780511526503

A. Bensoussan and H. Nagai, An ergodic control problem arising from the principal eigenfunction of an elliptic operator, Journal of the Mathematical Society of Japan, vol.43, issue.1, pp.49-65, 1991.
DOI : 10.2969/jmsj/04310049

T. Bielecki and S. Pliska, Risk-Sensitive Dynamic Asset Management, Applied Mathematics and Optimization, vol.39, issue.3, pp.337-360, 1999.
DOI : 10.1007/s002459900110

C. Blanchet-scalliet, N. Karoui, M. Jeanblanc, and L. Martellini, Optimal investment and consumption when time-horizon is uncertain, 2002.

O. Bobrovnytska and M. Schweizer, Mean-Variance Hedging and Stochastic Control: Beyond the Brownian Setting, IEEE Transactions on Automatic Control, vol.49, issue.3, pp.1-14, 2004.
DOI : 10.1109/TAC.2004.824468

V. Borkar, Optimal control of diffusion processes, Pitman Research Notes in Math, vol.203, 1989.

V. Borkar, Controlled diffusion processes, Probability surveys, pp.213-244, 2005.
DOI : 10.1214/154957805100000131

B. Bouchard and H. Pham, Wealth-path dependent utility maximization in incomplete markets, Finance and Stochastics, vol.8, issue.4, pp.579-603, 2004.
DOI : 10.1007/s00780-004-0125-8

URL : https://hal.archives-ouvertes.fr/hal-00102259

B. Bouchard and N. Touzi, Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, pp.175-206, 2004.
DOI : 10.1016/j.spa.2004.01.001

URL : https://hal.archives-ouvertes.fr/hal-00103046

K. Brekke and B. Oksendal, Optimal Switching in an Economic Activity under Uncertainty, SIAM Journal on Control and Optimization, vol.32, issue.4, pp.1021-1036, 1994.
DOI : 10.1137/S0363012992229835

M. Broadie, J. Cvitanic, and M. Soner, Optimal Replication of Contingent Claims under Portfolio Constraints, Review of Financial Studies, vol.11, issue.1, pp.59-79, 1998.
DOI : 10.1093/rfs/11.1.59

R. Carmona and N. Touzi, OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS, Mathematical Finance, vol.3767, issue.2, 2004.
DOI : 10.2307/2331121

U. Cetin, R. Jarrow, and P. Protter, Liquidity risk and arbitrage pricing theory, Finance and Stochastics, vol.8, issue.3, pp.311-341, 2004.
DOI : 10.1007/s00780-004-0123-x

M. Crandall, P. L. Ishii, and . Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

J. Cvitanic, H. Pham, and N. Touzi, Super-replication in stochastic volatility models under portfolio constraints, Journal of Applied Probability, vol.3, issue.02, pp.523-545, 1999.
DOI : 10.1111/j.1540-6261.1987.tb02568.x

J. Cvitanic, H. Pham, and N. Touzi, A closed-form solution to the problem of super-replication under transaction costs, Finance and Stochastics, vol.3, issue.1, pp.35-54, 1999.
DOI : 10.1007/s007800050051

M. Davis and P. Varaiya, Dynamic Programming Conditions for Partially Observable Stochastic Systems, SIAM Journal on Control, vol.11, issue.2, pp.226-261, 1973.
DOI : 10.1137/0311020

F. Delarue, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stochastic Processes and their Applications, vol.99, issue.2, pp.209-286, 2002.
DOI : 10.1016/S0304-4149(02)00085-6

F. Delarue and S. Menozzi, A forward???backward stochastic algorithm for quasi-linear PDEs, The Annals of Applied Probability, vol.16, issue.1, 2004.
DOI : 10.1214/105051605000000674

URL : https://hal.archives-ouvertes.fr/hal-00005448

J. Douglas, J. Ma, and P. Protter, Numerical methods for forward-backward stochastic differential equations, The Annals of Applied Probability, vol.6, issue.3, pp.940-968, 1996.
DOI : 10.1214/aoap/1034968235

K. Duckworth and M. Zervos, A Model for Investment Decisions with Switching Costs, The Annals of Applied Probability, vol.11, issue.1, pp.239-250, 2001.
DOI : 10.1214/aoap/998926992

E. Karoui and N. , Les Aspects Probabilistes Du Controle Stochastique, Lect. Notes in Math, vol.816, 1981.
DOI : 10.1007/BFb0097499

E. Karoui, N. , S. Peng, and M. C. Quenez, Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997.
DOI : 10.1111/1467-9965.00022

E. Karoui, N. , and M. C. Quenez, Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market, SIAM Journal on Control and Optimization, vol.33, issue.1, pp.29-66, 1995.
DOI : 10.1137/S0363012992232579

B. Fitzpatrick and W. Fleming, Numerical Methods for an Optimal Investment-Consumption Model, Mathematics of Operations Research, vol.16, issue.4, pp.823-841, 1991.
DOI : 10.1287/moor.16.4.823

W. Fleming, Optimal Control of Partially Observable Diffusions, SIAM Journal on Control, vol.6, issue.2, pp.194-214, 1968.
DOI : 10.1137/0306015

W. Fleming and D. Hernandez-hernandez, An optimal consumption model with stochastic volatility, Finance and Stochastics, vol.7, issue.2, pp.245-262, 2003.
DOI : 10.1007/s007800200083

W. Fleming and W. Mceneaney, Risk-Sensitive Control on an Infinite Time Horizon, SIAM Journal on Control and Optimization, vol.33, issue.6, pp.1881-1915, 1995.
DOI : 10.1137/S0363012993258720

W. Fleming and R. , Deterministic and stochastic optimal control, 1975.
DOI : 10.1007/978-1-4612-6380-7

W. Fleming and S. Sheu, Risk-Sensitive Control and an Optimal Investment Model, Mathematical Finance, vol.10, issue.2, pp.197-213, 2000.
DOI : 10.1111/1467-9965.00089

M. Fuhrman, Y. Hu, and G. Tessitore, On a Class of Stochastic Optimal Control Problems Related to BSDEs with Quadratic Growth, SIAM Journal on Control and Optimization, vol.45, issue.4, 2005.
DOI : 10.1137/050633548

URL : https://hal.archives-ouvertes.fr/hal-00451623

E. Gobet, J. P. Lemor, and X. Warin, A regression-based Monte Carlo method to solve backward stochastic differential equations, The Annals of Applied Probability, vol.15, issue.3, 2004.
DOI : 10.1214/105051605000000412

A. Gundel, Robust utility maximization for complete and incomplete market models, Finance and Stochastics, vol.9, issue.2, pp.151-176, 2004.
DOI : 10.1007/s00780-004-0148-1

X. Guo, An explicit solution to an optimal stopping problem with regime switching, Journal of Applied Probability, vol.39, issue.02, pp.464-481, 2001.
DOI : 10.1007/BF01450498

X. Guo and H. Pham, Optimal partially reversible investment with entry decision and general production function, Stoc. Proc. Appli, pp.705-736, 2005.
DOI : 10.1016/j.spa.2004.12.002

URL : https://hal.archives-ouvertes.fr/hal-00101851

H. Hata and J. Sekine, Solving a large deviations control problem with a nonlinear factor model, 2005.

Y. Hu and S. Peng, Solution of forward-backward stochastic differential equations, Probability Theory and Related Fields, vol.38, issue.2, pp.273-283, 1995.
DOI : 10.1007/BF01204218

M. Jeanblanc and A. Shiryaev, Optimization of the flow of dividends, Russian Mathematical Surveys, vol.50, issue.2, pp.257-277, 1995.
DOI : 10.1070/RM1995v050n02ABEH002054

Y. Kabanov and C. Kluppelberg, A geometric approach to portfolio optimization in models with transaction costs, Finance and Stochastics, vol.8, issue.2, pp.207-227, 2004.
DOI : 10.1007/s00780-003-0114-3

I. Karatzas, On a stochastic representation for the principal eigenvalue of a second order differential equation, Stochastics and Stochastics Reports, vol.3, pp.305-321, 1980.

M. Kobylanski, differential equations with quadratic growth, The Annals of Probability, vol.28, issue.2, pp.558-602, 2000.
DOI : 10.1214/aop/1019160253

M. Kohlmann and S. Tang, Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean???variance hedging, Stochastic Processes and their Applications, vol.97, issue.2, pp.255-288, 2002.
DOI : 10.1016/S0304-4149(01)00133-8

M. Kohlmann and X. Y. Zhou, Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach, SIAM Journal on Control and Optimization, vol.38, issue.5, pp.1392-1407, 2000.
DOI : 10.1137/S036301299834973X

R. Korn, Portfolio optimisation with strictly positive transaction costs and impulse control, Finance and Stochastics, vol.2, issue.2, pp.85-114, 1998.
DOI : 10.1007/s007800050034

N. Krylov, On the rate of convergence of finite-difference approximations for Bellmans equations with variable coefficients, Probability Theory and Related Fields, vol.117, issue.1, pp.1-16, 2000.
DOI : 10.1007/s004400050264

H. J. Kushner, Approximation and weak convergence methods for random processes, with applications to stochastic systems theory, Series in Signal Processing, Optimization , and Control, p.269, 1977.

H. J. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time, Stochastic Modelling and Applied Probability, p.475, 2001.

O. Ladyzhenskaya, V. Solonnikov, and N. Uralseva, Linear and quasilinear equations of parabolic type, 1968.

P. L. Lions, Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application, Communications in Partial Differential Equations, vol.9, issue.10, pp.1101-1134, 1983.
DOI : 10.1080/03605308308820297

P. L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: the case of bounded stochastic evolutions, Acta Mathematica, vol.161, issue.0, pp.243-278, 1988.
DOI : 10.1007/BF02392299

L. Vath, V. Mnif, M. , and H. Pham, A model of optimal portfolio selection under liquidity risk and price impact, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00011190

J. Ma, P. Protter, J. San-martin, and S. Torres, Numerical method for backward stochastic differential equations, Ann. Appl. Prob, vol.12, pp.302-316, 2002.

J. Ma, P. Protter, and J. Yong, Solving forward-backward stochastic differential equations explicitly ? a four step scheme, Probability Theory and Related Fields, vol.36, issue.3, pp.339-359, 1994.
DOI : 10.1007/BF01192258

J. Ma and J. Yong, Forward-backward stochastic differential equations and their applications, Lect. Notes in Math, vol.1702, 1702.
DOI : 10.1007/978-3-540-48831-6

M. Mania and R. Tevzadze, Backward Stochastic PDE and Imperfect Hedging, International Journal of Theoretical and Applied Finance, vol.06, issue.07, pp.663-692, 2003.
DOI : 10.1142/S0219024903002122

M. Nisio, Lectures on Stochastic Control Theory, ISI Lect. Notes, vol.9, 1981.

B. Oksendal and A. Sulem, Optimal Consumption and Portfolio with Both Fixed and Proportional Transaction Costs, SIAM Journal on Control and Optimization, vol.40, issue.6, pp.1765-1790, 2002.
DOI : 10.1137/S0363012900376013

B. Oksendal and A. Sulem, Applied stochastic control of jump diffusion, 2004.
DOI : 10.1007/978-3-540-69826-5

G. Pagès, H. Pham, and J. Printems, AN OPTIMAL MARKOVIAN QUANTIZATION ALGORITHM FOR MULTI-DIMENSIONAL STOCHASTIC CONTROL PROBLEMS, Stochastics and Dynamics, vol.04, issue.04, pp.501-545, 2004.
DOI : 10.1142/S0219493704001231

G. Pagès, H. Pham, and J. Printems, Optimal Quantization Methods and Applications to Numerical Problems in Finance, Handbook of computational and numerical methods in finance, 2004.
DOI : 10.1007/978-0-8176-8180-7_7

E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, vol.14, issue.1, pp.55-61, 1990.
DOI : 10.1016/0167-6911(90)90082-6

E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, Probability Theory and Related Fields, vol.114, issue.2, pp.123-150, 1999.
DOI : 10.1007/s004409970001

S. Peng, A General Stochastic Maximum Principle for Optimal Control Problems, SIAM Journal on Control and Optimization, vol.28, issue.4, pp.966-979, 1990.
DOI : 10.1137/0328054

H. Pham, On quadratic hedging in continuous time, Mathematical Methods of Operations Research (ZOR), vol.51, issue.2, pp.315-339, 2000.
DOI : 10.1007/s001860050091

H. Pham, Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints, Applied Mathematics and Optimization, vol.46, issue.1, pp.55-78, 2002.
DOI : 10.1007/s00245-002-0735-5

H. Pham, A large deviations approach to optimal long term investment, Finance and Stochastics, vol.7, issue.2, pp.169-195, 2003.
DOI : 10.1007/s007800200082

URL : https://hal.archives-ouvertes.fr/hal-00103816

H. Pham, A risk-sensitive control dual approach to a large deviations control problem, Systems & Control Letters, vol.49, issue.4, pp.295-309, 2003.
DOI : 10.1016/S0167-6911(03)00100-2

URL : https://hal.archives-ouvertes.fr/hal-00103978

H. Pham, On the Smooth-Fit Property for One-Dimensional Optimal Switching Problem, Séminaire de Probabilités, 2005.
DOI : 10.1007/978-3-540-71189-6_8

URL : https://hal.archives-ouvertes.fr/hal-00168849

H. Pham, Optimisation et contrôle stochastique appliquésappliquésà la finance, to appear, Series Mathématiques et Applications, 2005.

A. Schied, Optimal Investments for Robust Utility Functionals in Complete Market Models, Mathematics of Operations Research, vol.30, issue.3, 2003.
DOI : 10.1287/moor.1040.0138

M. Schweizer, A guided tour through quadratic hedging approaches " , in Option pricing , Interest rates and risk management, 2001.

S. Shreve and M. Soner, Optimal Investment and Consumption with Transaction Costs, The Annals of Applied Probability, vol.4, issue.3, pp.609-692, 1994.
DOI : 10.1214/aoap/1177004966

URL : http://repository.cmu.edu/cgi/viewcontent.cgi?article=1466&context=math

M. Soner and N. Touzi, Superreplication Under Gamma Constraints, SIAM Journal on Control and Optimization, vol.39, issue.1, pp.73-96, 2000.
DOI : 10.1137/S0363012998348991

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.1624

M. Soner and N. Touzi, Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions, SIAM Journal on Control and Optimization, vol.41, issue.2, pp.404-424, 2002.
DOI : 10.1137/S0363012900378863

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.6819

S. Tang and J. Yong, Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach, Stochastics and Stochastic Reports, vol.2, issue.3-4, pp.145-176, 1993.
DOI : 10.1007/BF01447655

A. Tourin and T. Zariphopoulou, Numerical schemes for investment models with singular transactions, Computational Economics, vol.30, issue.No. 3, pp.287-307, 1994.
DOI : 10.1007/BF01299457

J. Yong and X. Y. Zhou, Stochastic controls, Hamiltonian systems and HJB equations, 2000.

T. Zariphopoulou, Optimal investment-consumption models with constraints, 1988.

T. Zariphopoulou, A solution approach to valuation with unhedgeable risks, Finance and Stochastics, vol.5, issue.1, pp.61-82, 2001.
DOI : 10.1007/PL00000040

G. Zitkovic, Utility maximization with a stochastic clock and an unbounded random endowment, The Annals of Applied Probability, vol.15, issue.1B, pp.748-777, 2005.
DOI : 10.1214/105051604000000738

X. Y. Zhou, On the Necessary Conditions of Optimal Controls for Stochastic Partial Differential Equations, SIAM Journal on Control and Optimization, vol.31, issue.6, pp.1462-1478, 1993.
DOI : 10.1137/0331068