O. Alvarez, A quasilinear elliptic equation in ???N, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.31, issue.05, pp.911-921, 1996.
DOI : 10.1070/IM1982v019n01ABEH001410

O. Alvarez, Bounded-from-below viscosity solutions of Hamilton-Jacobi equations, Differential Integral Equations, vol.10, issue.3, pp.419-436, 1997.

M. Bardi and I. C. Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkhäuser Boston Inc, 1997.
DOI : 10.1007/978-0-8176-4755-1

M. Bardi and F. Da-lio, On the Bellman equation for some unbounded control problems, NoDEA : Nonlinear Differential Equations and Applications, vol.4, issue.4, pp.491-510, 1997.
DOI : 10.1007/s000300050027

G. Barles, An approach of deterministic control problems with unbounded data, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, issue.4, pp.235-258, 1990.
DOI : 10.1016/S0294-1449(16)30290-6

G. Barles, Solutions de viscosité deséquationsdeséquations de Hamilton-Jacobi, 1994.

G. Barles, S. Biton, M. Bourgoing, and O. Ley, Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods, Calculus of Variations and Partial Differential Equations, vol.18, issue.2, pp.159-179, 2003.
DOI : 10.1007/s00526-002-0186-5

G. Barles, J. Burdeau, M. Romano, and N. Samsoen, CRITICAL STOCK PRICE NEAR EXPIRATION, Mathematical Finance, vol.2, issue.2, pp.77-95, 1995.
DOI : 10.1086/295902

G. Barles and B. Perthame, Exit Time Problems in Optimal Control and Vanishing Viscosity Method, SIAM Journal on Control and Optimization, vol.26, issue.5, pp.1133-1148, 1988.
DOI : 10.1137/0326063

A. Bensoussan, Stochastic control by functional analysis methods, Mathematics and its Applications, 1982.

F. E. Benth and K. H. Karlsen, A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets, Stochastics An International Journal of Probability and Stochastic Processes, vol.5, issue.1, 2003.
DOI : 10.1093/rfs/4.4.727

P. Cannarsa and G. Da-prato, Nonlinear Optimal Control with Infinite Horizon for Distributed Parameter Systems and Stationary Hamilton???Jacobi Equations, SIAM Journal on Control and Optimization, vol.27, issue.4, pp.861-875, 1989.
DOI : 10.1137/0327046

M. G. Crandall and P. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983.
DOI : 10.1090/S0002-9947-1983-0690039-8

M. G. Crandall and P. Lions, Quadratic growth of solutions of fully nonlinear second order equations in IR n, Differential Integral Equations, vol.3, issue.4, pp.601-616, 1990.

M. G. Crandall, H. Ishii, and P. 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

F. , D. Lio, and W. M. Mceneaney, Finite time-horizon risk-sensitive control and the robust limit under a quadratic growth assumption, SIAM J. Control Optim, vol.40, issue.5, pp.1628-1661, 2002.

L. C. Evans, Partial differential equations, 1998.

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

W. H. Fleming and H. M. Soner, Controlled Markov processes and viscosity solutions, 1993.

H. Ishii, Perron's method for Hamilton-Jacobi equations. Duke Math, J, vol.55, issue.2, pp.369-384, 1987.

H. Ishii, Comparison results for hamilton-jacobi equations without grwoth condition on solutions from above, Applicable Analysis, vol.67, issue.3-4, pp.357-372, 1997.
DOI : 10.1137/S0363012994262695

K. Ito, Existence of Solutions to the Hamilton???Jacobi???Bellman Equation under Quadratic Growth Conditions, Journal of Differential Equations, vol.176, issue.1, pp.1-28, 2001.
DOI : 10.1006/jdeq.2000.3980

F. John, Partial differential equations, 1991.

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991.
DOI : 10.1007/978-1-4612-0949-2

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

N. V. Krylov, Controlled diffusion processes, of Applications of Mathematics, 1980.
DOI : 10.1007/978-1-4612-6051-6

N. V. Krylov, Stochastic Linear Controlled Systems with Quadratic Cost Revisited, Stochastics in finite and infinite dimensions, pp.207-232, 2001.
DOI : 10.1007/978-1-4612-0167-0_12

D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliquéappliquéà la finance, EllipsesÉditionEllipses´EllipsesÉdition Marketing, 1997.

O. Ley, Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts, Adv. Differential Equations, vol.6, issue.5, pp.547-576, 2001.

P. 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.1101-1174, 1983.
DOI : 10.1080/03605308308820297

P. Lions, Optimal control of diffusion processes and hamilton???jacobi???bellman equations part 2 : viscosity solutions and uniqueness, Communications in Partial Differential Equations, vol.25, issue.11, pp.1229-1276, 1983.
DOI : 10.1080/03605308308820301

P. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. III. Regularity of the optimal cost function, Nonlinear partial differential equations and their applications.Colì ege de France seminar, pp.95-205, 1981.

W. M. Mceneaney, Robust control and differential games on a finite time horizon, Mathematics of Control, Signals, and Systems, vol.39, issue.2, pp.138-166, 1995.
DOI : 10.1007/BF01210205

W. M. Mceneaney, Uniqueness for Viscosity Solutions of Nonstationary Hamilton???Jacobi???Bellman Equations under Some a Priori Conditions (with Applications), SIAM Journal on Control and Optimization, vol.33, issue.5, pp.1560-1576, 1995.
DOI : 10.1137/S0363012994262695

W. M. Mceneaney, A uniqueness result for the isaacs equation corresponding to nonlinear H??? control, Mathematics of Control, Signals, and Systems, vol.15, issue.4, pp.303-334, 1998.
DOI : 10.1007/BF02750395

H. Nagai, Bellman Equations of Risk-Sensitive Control, SIAM Journal on Control and Optimization, vol.34, issue.1, pp.74-101, 1996.
DOI : 10.1137/S0363012993255302

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

F. Rampazzo and C. Sartori, Hamilton-Jacobi-Bellman equations with fast gradient-dependence, Indiana University Mathematics Journal, vol.49, issue.3, pp.1043-1077, 2000.
DOI : 10.1512/iumj.2000.49.1736
URL : http://doi.org/10.1512/iumj.2000.49.1736

J. Yong and X. Y. Zhou, Stochastic controls, volume 43 of Applications of Mathematics, 1999.