O. Alvarez and E. N. Barron, Homogenization in L ?, J. of Differential Equations, vol.183, pp.132-164, 2002.

L. S. Aragone and R. L. González, A Bellman's equation for minimizing the maximum cost, Indian J. of Pure and Applied Mathematics, vol.31, issue.12, pp.1621-1632, 2000.

M. Assellaou, O. Bokanowski, A. Désilles, and H. Zidani, Value function and optimal trajectories for a maximum running cost control problem with state constraints. application to an abort landing problem, p.2, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01484190

G. Barles, C. Daher, and M. Romano, Convergence of numerical schemes for parabolic equations arising in finance theory, SIAM J. Control Optim, vol.32, issue.3, pp.125-143, 1994.

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

E. N. Barron, The Bellman equation for control of the running max of a diffusion and applications to lookback options, Viscosity solutions and Analysis in L ? , Proceeding of the NATO advanced study Institute, vol.48, pp.1-60, 1993.

E. N. Barron and H. Ishii, The Bellman equation for minimizing the maximum cost, Nonlinear Analysis, vol.13, issue.9, pp.1067-1090, 1989.

P. Bettiol and F. Rampazzo, control problems as dynamic differential games, Nonlinear Differential Equations and Applications NoDEA, vol.20, issue.3, pp.895-918, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01067311

O. Bokanowski, A. Picarelli, and H. Zidani, Dynamic programming and error estimates for stochastic control problems with maximum cost, Applied Mathematics and Optimization, vol.71, issue.1, pp.125-163, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00931025

J. F. Bonnans, E. Ottenwaelter, and H. Zidani, Numerical schemes for the two dimensional second-order HJB equation, ESAIM, pp.723-735, 2004.

J. F. Bonnans and H. Zidani, Consistency of generalized finite difference schemes for the stochastic HJB equation, SIAM J. Numerical Analysis, vol.41, issue.3, pp.1008-1021, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00072460

B. Bouchard and N. Touzi, Weak dynamic programming principle for viscosity solutions, SIAM J. Control and Optimization, vol.49, issue.3, pp.948-962, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00367355

F. Camilli and M. Falcone, An approximation scheme for the optimal control of diffusion processes, RAIRO Modél. Math. Anal. Numér, vol.29, issue.1, pp.97-122, 1995.

I. Capuzzo-dolcetta, On a discrete approximation of the hamilton-jacobi equation of dynamic programming, Applied Mathematics and Optimization, vol.10, pp.367-377, 1983.

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

M. G. Crandall and P. L. Lions, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion, Mathematics of Computation, vol.75, issue.1, pp.17-41, 1996.

K. Debrabant and E. R. Jakobsen, Semi-Lagrangian schemes for linear and fully nonlinear diffusion equations, Mathematics of Computation, vol.82, issue.283, pp.1433-1462, 2012.

S. C. Di-marco and R. L. González, Rapport de Recherche N. 2945, INRIA, Rocquencourt, 1996. 21. , Supersolutions and subsolutions techniques in a minimax optimal control problem with infinite horizon, Indian J. of Pure and Applied Mathematics, vol.29, issue.10, 1983.

P. Dupuis and H. Ishii, On oblique derivative problems for fully nonlinear second-order elliptic PDE's on domains with corners, Hokkaido Mathematical Journal, vol.20, issue.1, pp.135-164, 1991.

D. Goreac and O. Serea, Linearization techniques for L ?-control problems and dynamic programming principles in classical and L ?-controlproblems, pp.836-855, 2012.

L. Grüne and A. Picarelli, Zubov's method for controlled diffusions with state constraints, Nonlinear Differential Equations and Applications, vol.22, issue.6, pp.1765-1799, 2015.

L. Grüne and H. Zidani, Zubov's equation for state-constrained perturbed nonlinear systems, Math. Control Related Fields, vol.5, issue.1, pp.55-71, 2015.

A. C. Heinricher and R. H. Stockbridge, Optimal control of the running max, SIAM J. Control and Optimization, vol.29, issue.4, pp.936-953, 1991.

H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear secondorder elliptic PDEs, Communications in Pure and Applied Mathematics, vol.42, issue.3, pp.633-661, 1989.

M. Jones and M. Peet, Solving dynamic programming with supremum terms in the objective and application to optimal battery scheduling for electricity consumers subject to demand charges, IEEE 56th Annual Conference on Decision and Control, 2017.

H. J. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time

P. L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part I: The Dynamic Programming principle and applications, Communications in Partial Differential Equations, vol.8, issue.10, pp.1101-1174, 1983.

J. L. Menaldi, Some estimates for finite difference approximations, SIAM J. Control and Optimization, vol.27, pp.579-607, 1989.

R. Munos and H. Zidani, Consistency of a simple multidimensional scheme for Hamilton-Jacobi-Bellman equations, Comptes Rendus Mathématique, vol.340, issue.7, pp.499-502, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00983347

M. Quincampoix and O. Serea, A viability approach for optimal control with infimum cost, Annals of the, Alexandru Ioan Cuza" University of Iasi, vol.48, issue.1, pp.113-132, 2002.

O. Serea, Discontinuous differential games and control systems with supremum cost, Journal of Mathematical Analysis and Applications, vol.270, issue.2, pp.519-542, 2002.

N. Touzi, Optimal stochastic control, stochastic target problems, and backward SDE, Fields Institute Monographs, vol.49, 2012.