A. [. Alili and . Kyprianou, Some remarks on first passage of L??vy processes, the American put and pasting principles, The Annals of Applied Probability, vol.15, issue.3, pp.2062-2080, 2005.
DOI : 10.1214/105051605000000377

Z. Artstein, Compact convergence of ?-fields and relaxed conditional expectation. Probability Theory and Related Fields, pp.369-394, 2001.

I. [. Abramowitz and . Stegun, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, 1972.

]. E. Bal84 and . Balder, A general approach to lower semicontinuity and lower closure in optimal control theory On Prohorov's theorem for transition probabilities, SIAM journal on control and optimization Sém. Anal. Convexe, vol.22, issue.11, pp.570-598, 1984.

]. E. Bal00 and . Balder, Lectures on Young measure theory and its applications in economics

]. K. Bar04 and . Barty, Contributions à la discretisation des contraintes de mesurabilité pour les problèmes d'optimisation stochastique, 2004.

B. Bouchard, R. Elie, and C. Imbert, Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol.48, issue.5
DOI : 10.1137/090757629

URL : https://hal.archives-ouvertes.fr/hal-00373306

]. R. Bel52 and . Bellman, On the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A, vol.38, pp.716-719, 1952.

]. R. Bel54 and . Bellman, The theory of dynamic programming, Bull. Amer. Math. Soc, vol.60, pp.503-515, 1954.

]. R. Bel57 and N. J. Bellman, Dynamic programming REFERENCES [Ben84] A. Bensoussan. On the theory of option pricing, Acta Applicandae Mathematicae, vol.2, issue.2, pp.139-158, 1957.

]. J. Ber96 and . Bertoin, Lévy processes, volume 121 of Cambridge Tracts in Mathematics, 1996.

]. D. Ber01 and . Bertsekas, Dynamic programming and optimal control, Athena Scientific, vol.I, 2001.

R. [. Bouchard, N. Elie, and . Touzi, Stochastic Target Problems with Controlled Loss, SIAM Journal on Control and Optimization, vol.48, issue.5
DOI : 10.1137/08073593X

URL : https://hal.archives-ouvertes.fr/hal-00323383

H. Berliocchi and J. Lasry, Int??grandes normales et mesures param??tr??es en calcul des variations, Bulletin de la Société mathématique de France, vol.79, pp.129-184, 1973.
DOI : 10.24033/bsmf.1755

]. N. Bou71 and . Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, 1971.

U. [. Bäuerle and . Rieder, Markov Decision Processes, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol.112, issue.4, pp.217-243, 2010.
DOI : 10.1365/s13291-010-0007-2

S. [. Bertsekas and . Shreve, Stochastic optimal control The discrete time case, Mathematics in Science and Engineering, vol.139, 1978.

P. [. Borodin and . Salminen, Handbook of Brownian motion?facts and formulae. Probability and its Applications, 1996.

H. [. Bayraktar and . Xing, Analysis of the Optimal Exercise Boundary of American Options for Jump Diffusions, SIAM Journal on Mathematical Analysis, vol.41, issue.2, pp.825-8601613, 2006.
DOI : 10.1137/080712519

J. P. Carpentier, G. Chancelier, M. Cohen, P. Lara, and . Girardeau, Dynamic consistency for stochastic optimal control problems, Annals of Operations Research, vol.7, issue.1, pp.1-17, 2011.
DOI : 10.1007/s10479-011-1027-8

URL : https://hal.archives-ouvertes.fr/hal-00483811

J. [. Chen, L. Chadam, W. Jiang, and . Zheng, CONVEXITY OF THE EXERCISE BOUNDARY OF THE AMERICAN PUT OPTION ON A ZERO DIVIDEND ASSET, Mathematical Finance, vol.7, issue.1, pp.185-197, 2008.
DOI : 10.1111/j.1467-9965.2007.00328.x

P. Carr, R. Jarrow, and R. Myneni, ALTERNATIVE CHARACTERIZATIONS OF AMERICAN PUT OPTIONS, Mathematical Finance, vol.6, issue.2, pp.87-106, 1992.
DOI : 10.1007/BF00250676

C. Castaing, P. Raynaud-de-fitte, and M. Valadier, Young measures on topological spaces, volume 571 of Mathematics and its Applications, 2004.

H. [. Chow, D. Robbins, and . Siegmund, Great expectations: the theory of optimal stopping, 1971.

P. [. Cont and . Tankov, Financial modelling with jump processes, CRC Financial Mathematics Series. Chapman & Hall/CRC, vol.2, 2004.
DOI : 10.1201/9780203485217

URL : https://hal.archives-ouvertes.fr/hal-00002693

M. [. Castaing and . Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, vol.580, 1977.
DOI : 10.1007/BFb0087685

J. [. Dvoretzky, J. Kiefer, and . Wolfowitz, The Inventory Problem: I. Case of Known Distributions of Demand, Econometrica, vol.20, issue.2, pp.187-222, 1952.
DOI : 10.2307/1907847

C. Dellacherie and P. A. Meyer, Probabilités et potentiel Chapitres I à IV, Édition entièrement refondue, Publications de l, XV, Actualités Scientifiques et Industrielles, No. 1372. [Dyn63] E. B. Dynkin. Optimal choice of the stopping moment of a Markov process. Dokl. Akad, 1975.

. [. Karoui, Les Aspects Probabilistes Du Controle Stochastique, Lecture Notes in Math, vol.876, pp.73-238, 1979.
DOI : 10.1007/BFb0097499

E. [. Karoui, M. C. Pardoux, and . Quenez, Reflected Backward SDEs and American Options, Numerical methods in finance, pp.215-231
DOI : 10.1017/CBO9781139173056.012

]. E. Eks04 and . Ekström, Convexity of the optimal stopping boundary for the american put option, Journal of Mathematical Analysis and Applications, vol.229, issue.1, pp.147-156, 2004.

]. I. Evs76 and . Evstigneev, Measurable selection and dynamic programming, Mathematics of Operations Research, vol.1, issue.3, pp.267-272, 1976.

]. K. Fan53 and . Fan, Minimax Theorems, Proceedings of the National Academy of Sciences, vol.39, issue.1, p.42, 1953.
DOI : 10.1073/pnas.39.1.42

]. A. Fri88 and . Friedman, Variational principles and free-boundary problems, 1988.

H. [. Fleming and . Soner, Controlled Markov processes and viscosity solutions Résolution de grands problèmes en optimisation stochastique dynamique et synthèse de lois de commande, Applications of Mathematics, vol.25, 1993.

R. E. Göttsche and M. H. Vellekoop, THE EARLY EXERCISE PREMIUM FOR THE AMERICAN PUT UNDER DISCRETE DIVIDENDS, Mathematical Finance, vol.15, issue.2, pp.335-354, 2011.
DOI : 10.1111/j.1467-9965.2010.00427.x

]. S. Jac93 and . Jacka, Local , optimal stopping and semimartingales, Annals of Probability, vol.21, pp.329-339, 1993.

B. [. Jeunesse and . Jourdain, Regularity of the American Put option in the Black?Scholes model with general discrete dividends. Stochastic Process, Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends. SIAM Journal on Mathematical Finance, pp.3101-3125538, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00633199

]. O. Kal02 and . Kallenberg, Foundations of modern probability. Probability and its Applications, 2002.

P. [. Kushner and . Dupuis, Numerical methods for stochastic control problems in continuous time, 2000.

]. I. Kim90 and . Kim, The Analytic Valuation of American Options, Review of Financial Studies, vol.3, issue.4, pp.547-572, 1990.
DOI : 10.1093/rfs/3.4.547

C. [. Kuratowski, A general theorem on selectors, Bull. Acad

S. [. Karatzas and . Shreve, Methods of mathematical finance [Lam95] D. Lamberton. Critical price for an American option near maturity, Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, pp.353-358, 1991.

B. [. Lamberton and . Lapeyre, Introduction to stochastic calculus applied to finance

M. [. Lamberton and . Mikou, The critical price for the American put in??an??exponential L??vy model, Finance and Stochastics, vol.22, issue.4, pp.561-581, 2008.
DOI : 10.1007/s00780-008-0073-9

]. D. Lm12a, M. Lamberton, and . Mikou, Exercise boundary of the american put near maturity in an exponential lévy model, Finance and Stochastics, pp.1-40, 2012.

]. D. Lm12b, M. Lamberton, and . Mikou, The smooth-fit property in an exponential Lévy model, J

S. [. Lamberton and . Villeneuve, Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab, vol.13, issue.2, pp.800-815, 2003.

]. H. Mck65 and . Mckean, Appendix: a free boundary problem for the heat equation arising from a problem of mathematical economics, Ind. Management Rev, vol.6, pp.32-39, 1965.

]. Mey78 and . Meyer, Convergence faible et compacité des temps d'

]. V. Mik58 and . Mikhalevich, Sequential bayes solutions and optimal methods of statistical acceptance control, Theory Probab. Appl, vol.1, pp.395-421, 1958.

]. E. Mor02 and . Mordecki, Optimal stopping and perpetual options for Lévy processes, Finance Stoch, vol.6, issue.4, pp.473-493, 2002.

P. [. Mordecki and . Salminen, Optimal stopping of Hunt and L??vy processes, Stochastics An International Journal of Probability and Stochastic Processes, vol.73, issue.3-4, pp.233-251, 2007.
DOI : 10.1002/mana.19851240107

]. R. Myn92 and . Myneni, The pricing of the American option, Ped97] P. Pedregal. Parametrized measures and variational principles, pp.1-23, 1992.

]. P. Ped99 and . Pedregal, Optimization, relaxation and young measures, BULLETIN-AMERICAN MATHEMATICAL SOCIETY, vol.36, pp.27-58, 1999.

]. G. Pes05 and . Peskir, On the american option problem [Pha97] H. Pham. Optimal stopping, free boundary, and American option in a jump-diffusion model, Mathematical Finance Appl. Math. Optim, vol.15, issue.352, pp.169-181145, 1997.

]. H. Pha09 and . Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, 2009.

A. [. Pennanen and . Perkkiö, Stochastic programming without duality gaps, 2011.

]. L. Pra90 and . Pratelli, Sur le lemme de mesurabilité de Doob Optimal stopping and free-boundary problems, Séminaire de Probabilités, XXIV, pp.46-51, 1988.

]. M. Put94 and . Puterman, Markov decision processes: Discrete stochastic dynamic programming

]. U. Rie78 and . Rieder, Measurable selection theorems for optimization problems, Manuscripta Math, vol.24, issue.1, pp.115-131, 1978.

]. R. Roc76 and . Rockafellar, Integral functionals, normal integrands and measurable selections, Nonlinear operators and the calculus of variations, 1975.

R. [. Rockafellar and . Wets, Variational analysis, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1998.
DOI : 10.1007/978-3-642-02431-3

M. [. Revuz, . N. Yorshi08-]-a, and . Shiryaev, Continuous martingales and brownian motion Optimal stopping rules, of Stochastic Modelling and Applied Probability, 1991.

]. J. Sne52 and . Snell, Applications of martingale system theorems, Trans. Amer. Math. Soc, vol.73, pp.293-312, 1952.

]. H. St02a, N. Soner, and . Touzi, Dynamic programming for stochastic target problems and geometric flows, J. Eur. Math. Soc. (JEMS), vol.4, issue.3, pp.201-236, 2002.

]. H. St02b, N. Soner, and . Touzi, Stochastic target problems, dynamic programming, and viscosity solutions, SIAM J. Control Optim, vol.41, issue.2, pp.404-424, 2002.

]. L. Thi81 and . Thibault, Espérances conditionnelles d'intégrandes semi-continus, Ann. Inst. H

]. C. Vil and . Villani, Integration et analyse de fourier

. [. Van-moerbeke, On optimal stopping and free boundary problems, Archive for Rational Mechanics and Analysis, vol.60, issue.2, pp.101-148, 1976.
DOI : 10.1007/BF00250676

. H. Vn06-]-m, J. W. Vellekoop, and . Nieuwenhuis, Efficient pricing of derivatives on assets with discrete dividends, Applied Mathematical Finance, vol.13, issue.3, pp.265-284, 2006.

. H. Vn11-]-m, J. W. Vellekoop, and . Nieuwenhuis, An integral equation for American put options on assets with general dividend processes, Wal47] A. Wald. Sequential Analysis, pp.555-567, 1947.

J. [. Wald and . Wolfowitz, Bayes Solutions of Sequential Decision Problems, Proc. Nat
DOI : 10.1073/pnas.35.2.99

[. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, classe III, pp.212-234, 1937.