R. A. Adams, Sobolev Spaces, 1975.

A. Bensoussan, On the theory of option, Acta applicandae mathematicae, vol.2, pp.139-158, 1984.

A. Bensoussan and J. Lions, Applications des in equations variationnelles en contr^ ole stochastique, 1978.

A. Bensoussan and J. Lions, Contr^ ole impulsionnel et in equations quasi variationnelles, 1982.

F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.635-654, 1973.
DOI : 10.1086/260062

H. Bonnaz, P. Micottis, L. Tollie, A. Vanney, and G. Vinaver, Valorisation et couverture d'options sur actifs avec sauts poissoniens, 1989.

N. Bouleau and D. Lamberton, Residual risks and hedging strategies in Markovian markets, Stochastic Processes and their Applications, vol.33, issue.1, pp.131-150, 1989.
DOI : 10.1016/0304-4149(89)90071-9

URL : https://hal.archives-ouvertes.fr/hal-00017929

M. J. Brennan and E. S. Schwartz, The Valuation of American Put Options, The Journal of Finance, vol.32, issue.2, pp.449-462, 1977.
DOI : 10.2307/2326779

H. Brezis, Analyse fonctionnelle, th eorie et applications, 1983.

B. David, R. J. Colwell, and . Elliott, Martingale representation and non-attainable contingent claims

R. W. Cottle, J. S. Pang, and R. E. Stone, The Linear Complementarity Problem, 1992.

R. W. Cottle and R. S. Sacher, On the solution of large, structured linear complementarity problems: The tridiagonal case, Applied Mathematics & Optimization, vol.5, issue.4, pp.321-340, 1977.
DOI : 10.1007/BF01448184

C. John, M. Cox, and . Rubinstein, Options Markets, p.188, 1985.

C. W. Cryer, The eecient solution of linear complementarity problems for tridiagonal minkowski matrices, ACM Trans. Math. Softwave, vol.9, 1983.

C. Dol-eans-dade, Quelques applications de la formule de changement de variables pour les semimartingales, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.30, issue.3, 1970.
DOI : 10.1007/BF00534595

N. Karoui, Analyse nanci ere et probabilit es

N. Karoui and M. C. Quenez, Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market, SIAM Journal on Control and Optimization, vol.33, issue.1, 1991.
DOI : 10.1137/S0363012992232579

C. M. Elliott and J. R. Ockendon, Weak and Variational Methods for Moving Boundary Problems, 1982.

R. J. Elliott, Stochastic Calculus and Applications, 1982.

H. Ff-ollmer and M. Schweizer, Hedging of contingent claims under incomplete information, 1990.

H. Ff-ollmer and D. Sondermann, Hedging of non redundant contingent claims, Contributions to Mathematical Economics in Honor of Gerard Debreu, 1986.

P. Jaillet, D. Lamberton, and B. Lapeyre, Analyse num erique des options am ericaines, pp.66-126, 1988.

P. Jaillet, D. Lamberton, and B. Lapeyre, Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990.
DOI : 10.1007/BF00047211

I. Karatzas, On the pricing of American options, Applied Mathematics & Optimization, vol.60, issue.1, 1987.
DOI : 10.1007/BF01448358

O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Uralceva, Linear and quasilinear equations of parabolic type. Translations of mathematical monographs, 1968.

D. Lamberton and B. Lapeyre, Probabilit es num eriques et th eorie des options, Probabilit es Num eriques. Collection Didactique de l'INRIA, 1991.

D. Lamberton and B. Lapeyre, Introduction au Calcul Stochastique Appliqu e a la Finance . Ellipses-Edition Marketing, 1992.

C. E. Lemke, Bimatrix Equilibrium Points and Mathematical Programming, Management Science, vol.11, issue.7, pp.681-689, 1965.
DOI : 10.1287/mnsc.11.7.681

L. Macmillan, Analytic approximation for the american put option Advances in Futures and Options Research, pp.119-139, 1986.

R. C. Merton, Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, vol.4, issue.1, pp.141-183, 1973.
DOI : 10.2307/3003143

R. C. Merton, Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, vol.3, issue.1-2, pp.125-144, 1976.
DOI : 10.1016/0304-405X(76)90022-2

K. Murty, Linear Complementarity, Linear and Nonlinear Programming, Number 3 in Sigma Series in Applied Mathematics. Heldermann Verlag Berlin, 1988.

R. Myneni, The price of the american option, Annals of Applied Probability, 1992.

J. Neveu, Bases Math ematiques du Calcul des Probabilit es, 1964.

P. Protter, Stochastic Integration and Diierential Equations, Number 21 in Applications of Mathematics, 1990.

M. C. Quenez, M ethodes de contr^ ole stochastique en Finance, Th ese de l'universit e de Paris VI, 1993.

R. Saigal, A note on a special linear complementary problem, Opsearch, vol.7, pp.175-183, 1970.

M. Schweizer, Hedging Of Options In A General Semimartingale Model. Thesis Of Swiss Federal Institute Of Technology Zurich, 1988.

M. Schweizer, Option hedging for semi-martingales, Stochastic Processes and their Applications, pp.339-363, 1991.
DOI : 10.1016/0304-4149(91)90053-f

URL : http://doi.org/10.1016/0304-4149(91)90053-f

M. Schweizer, Some remarks on hedging under incomplete information

X. L. Zhang, Options am ericaines et mod eles de diiusion avec saut, Note aux Comptes Rendus de l'Acad emie des Sciences, pp.857-862, 1993.

X. L. Zhang, Formules quasi-explicites pour les options am ericaines dans un mod ele de diiusion avec sauts, Actes du Colloque Probabilit es Num eriques. a para^ tre, 1993.
DOI : 10.1016/0378-4754(93)e0078-j