Y. Achdou and O. Pironneau, Computational methods for option pricing, Frontiers in applied mathematics. SIAM, 2005.
DOI : 10.1137/1.9780898717495

URL : https://hal.archives-ouvertes.fr/hal-00111740

M. Akian, J. Menaldi, and A. Sulem, On an Investment-Consumption Model with Transaction Costs, SIAM Journal on Control and Optimization, vol.34, issue.1, pp.329-364, 1996.
DOI : 10.1137/S0363012993247159

G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, pp.271-283, 1991.
DOI : 10.1109/CDC.1990.204046

R. Bellman, FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING. V. POSITIVITY AND QUASI-LINEARITY, Proc. Nat. Acad. Sci. USA, pp.743-746, 1955.
DOI : 10.1073/pnas.41.10.743

R. Bellman, Dynamic programming, 1961.

M. Bergounioux, M. Hintermüller, and K. Kunisch, Primal-Dual Strategy for Constrained Optimal Control Problems, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1176-1194, 1999.
DOI : 10.1137/S0363012997328609

URL : https://hal.archives-ouvertes.fr/hal-00022023

O. Bokanowski, B. Bruder, S. Maroso, and H. Zidani, Numerical approximation of a superreplication problem under gamma constraints. in preparation, 2007.

J. F. Bonnans and P. Rouchon, Commande et optimisation de systèmes dynamiques. LeséditionsLeséditions de l'´ ecole polytechnique, 2005.

J. Chancelier, B. Øksendal, and A. Sulem, Combined stochastic control and optimal stopping, and application to numerical approximation of combined stochastic and impulse control, Tr. Mat. Inst. SteklovaStokhast. Finans. Mat, vol.237, pp.149-172, 2002.

M. Hintermuller, K. Ito, and K. Kunish, The Primal-Dual Active Set Strategy as a Semismooth Newton Method, SIAM Journal on Optimization, vol.13, issue.3, pp.865-888, 2002.
DOI : 10.1137/S1052623401383558

R. A. Howard, Dynamic programming and Markov processes. The Technology Press of the MIT, J. Wiley. Cambridge MA, 1960.

K. Ito and K. Kunish, Optimal Control of Elliptic Variational Inequalities, Applied Mathematics and Optimization, vol.41, issue.3, pp.343-364, 2000.
DOI : 10.1007/s002459911017

K. Ito and K. Kunish, Semi-smooth newton methods for variationnal inequalities of the first kind, pp.41-62, 2003.

K. Ito and K. Kunish, Parabolic variational inequalities: The Lagrange multiplier approach, Journal de Math??matiques Pures et Appliqu??es, vol.85, issue.3, pp.415-449, 2006.
DOI : 10.1016/j.matpur.2005.08.005

D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliquéappliqué`appliquéà la finance, Ellipses, 1997.

M. Mnif and A. Sulem, Optimal risk control and dividend policies under excess of loss reinsurance, Stochastics An International Journal of Probability and Stochastic Processes, vol.8, issue.5, pp.455-476, 2005.
DOI : 10.1214/aoap/1019737674

H. Pham, Optimal stopping, free boundary, and American option in a jump-diffusion model, Applied Mathematics & Optimization, vol.60, issue.2, pp.145-164, 1997.
DOI : 10.1007/BF02683325

H. Pham, Optimisation et Contrôle Stochastique AppliquésAppliqués`Appliquésà la Finance

M. L. Puterman and S. L. Brumelle, On the Convergence of Policy Iteration in Stationary Dynamic Programming, Mathematics of Operations Research, vol.4, issue.1, pp.60-69, 1979.
DOI : 10.1287/moor.4.1.60

M. S. Santos, Accuracy of Numerical Solutions Using the Euler Equation Residuals, Econometrica, vol.68, issue.6, pp.1377-1402, 2000.
DOI : 10.1111/1468-0262.00165

M. S. Santos and J. Rust, Convergence Properties of Policy Iteration, SIAM Journal on Control and Optimization, vol.42, issue.6, pp.2094-2115, 2004.
DOI : 10.1137/S0363012902399824

I. Unité-de-recherche, . Lorraine, . Loria, and . Technopôle-de-nancy, Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex