, A general Hamilton-Jacobi framework for non-linear state-constrained control problems, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.2, 2013.
DOI : 10.1051/cocv/2012011
, Stochastic viability and invariance, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.595, issue.4, pp.613-630, 1990.
, The viability theorem for stochastic differential inclusions. Stochastic Anal, 1998.
, Optimal Control on the $L^\infty $ Norm of a Diffusion Process, SIAM Journal on Control and Optimization, vol.32, issue.3, pp.10-1137, 1994.
DOI : 10.1137/S0363012991223595
, Convergence of numerical schemes for parabolic equations arising in finance theory, Math. Models Methods Appl. Sci, 1995.
, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations, M2AN Math. Model. Numer. Anal. DOI: 10.1051, p.2002, 2002.
DOI : 10.1051/m2an:2002002
, Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations, SIAM J. Numer. Anal, pp.10-1137, 2005.
DOI : 10.1137/s003614290343815x
URL : https://hal.archives-ouvertes.fr/hal-00017877
, Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations, Mathematics of Computation, vol.76, issue.260, 2007.
DOI : 10.1090/S0025-5718-07-02000-5
URL : https://hal.archives-ouvertes.fr/hal-00017877
, Fully nonlinear Neumann type boundary conditions for first-order Hamilton-Jacobi equations. Nonlinear Anal. Theory Methods Appl, pp.10-1016, 1991.
, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal. DOI: 10, pp.1991-4305, 1991.
, The Bellman equation for control of the running max of a diffusion and applications to lookback options, Appl. Anal, 1993.
, Reachability and Minimal Times for State Constrained Nonlinear Problems without Any Controllability Assumption, SIAM Journal on Control and Optimization, vol.48, issue.7, 2010.
DOI : 10.1137/090762075
URL : https://hal.archives-ouvertes.fr/hal-00395589
, Error estimates for stochastic differential games: the adverse stopping case, IMA Journal of Numerical Analysis, vol.26, issue.1, 2006.
DOI : 10.1093/imanum/dri034
URL : https://hal.archives-ouvertes.fr/inria-00070566
, Error bounds for a Stochastic Impulse Control Problem, Appl. Math Optim, 2007.
, Numerical schemes for the two dimensional second-order HJB equation, pp.2-735, 2004.
, Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation, SIAM Journal on Numerical Analysis, vol.41, issue.3, pp.10-1137, 2003.
DOI : 10.1137/S0036142901387336
URL : https://hal.archives-ouvertes.fr/inria-00072460
, Stochastic targets with mixed diffusion processes and viscosity solutions. Stochastic Processes and their Applications DOI: 10, pp.304-414900129, 1016.
DOI : 10.1016/s0304-4149(02)00129-1
URL : http://doi.org/10.1016/s0304-4149(02)00129-1
, Weak Dynamic Programming Principle for Viscosity Solutions, SIAM Journal on Control and Optimization, vol.49, issue.3, 2011.
DOI : 10.1137/090752328
URL : https://hal.archives-ouvertes.fr/hal-00367355
, An approximation scheme for the optimal control of diffusion processes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.29, issue.1, pp.122-151, 1995.
DOI : 10.1051/m2an/1995290100971
, On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming, Appl. Math. Optim, pp.10-1007, 1983.
, user's guide to viscosity solutions\\ of second order\\ partial
differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5
, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp. DOI:10.2307, 1984.
DOI : 10.1090/S0025-5718-1984-0744921-8
, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion, Numerische Mathematik, vol.75, issue.1, 1996.
DOI : 10.1007/s002110050228
, Semi-Lagrangian schemes for linear and fully non-linear diffusion equations, Mathematics of Computation, vol.82, issue.283, 2013.
DOI : 10.1090/S0025-5718-2012-02632-9
, On oblique derivative problems for fully nonlinear secondorder elliptic partial differential equations on nonsmooth domains. Nonlinear Anal. Theory Methods Appl, pp.10-1016, 1990.
, Optimal Control of the Running Max, SIAM Journal on Control and Optimization, vol.29, issue.4, 1991.
DOI : 10.1137/0329052
, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.105, issue.1, pp.135-151, 1989.
, Fully nonlinear oblique derivative problems for nonlinear Second-order elliptic PDEs. Duke Math, 1991.
, Viscosity solutions of fully nonlinear Second-order elliptic partial differential equations. J. Differential equations DOI: 10, pp.22-039690068, 1016.
, On the rate of convergence of finite-difference approximations for Bellman's equations, St. Petersburg Math. J, vol.639, issue.3, pp.650-659, 1998.
, On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients, 2000.
, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, 1977.
, Numerical methods for stochastic control problems in continuous time, 2001.
, Neumann type boundary conditions for Hamilton-Jacobi equations. Duke Math, 1985.
, Some Estimates for Finite Difference Approximations, SIAM Journal on Control and Optimization, vol.27, issue.3, 1989.
DOI : 10.1137/0327031
, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.10-1016, 1988.
DOI : 10.1016/0021-9991(88)90002-2
, Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions, SIAM Journal on Control and Optimization, vol.41, issue.2, pp.10-1137, 2002.
DOI : 10.1137/S0363012900378863
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.6819
, Paul Wilmott on quantitative finance, 2000.
, Stochastic controls: Hamiltonian systems and HJB equations Stochastic Modeling and Applied Probability, 1999.
DOI : 10.1007/978-1-4612-1466-3