Computational methods for option pricing, Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics, vol.30, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00019751
Estimation de la frontière libre des options américaines au voisinage de l'échéance, C. R. Acad. Sci. Paris Sér. I Math, vol.316, issue.2, pp.171-174, 1993. ,
Finite volume methods for the valuation of American options, M2AN Math. Model. Numer. Anal, vol.40, issue.2, pp.311-330, 2006. ,
On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, J. Math. Pures Appl, vol.85, issue.9, pp.371-414, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00004421
Some convergence results for Howard's algorithm, SIAM J. Numer. Anal, vol.47, issue.4, pp.3001-3026, 2009. ,
Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01628040
Introduction à l'analyse numérique matricielle et à l'optimisation. Collection Mathématiques Appliquées pour la Maîtrise ,
, , 1982.
User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), vol.27, issue.1, pp.1-67, 1992. ,
Analyse numérique des équations différentielles. Collection Mathématiques Appliquées pour la Maîtrise ,
, , 1984.
Integration of stiff equations, Proc. Nat. Acad. Sci. U. S. A, vol.38, pp.235-243, 1952. ,
Some mathematical results in the pricing of American options, European J. Appl. Math, vol.4, issue.4, pp.381-398, 1993. ,
Stability and error of the variable two-step BDF for semilinear parabolic problems, J. Appl. Math. & Computing, vol.19, issue.1-2, pp.33-55, 2005. ,
Quadratic convergence for valuing American options using a penalty method, SIAM J. Sci. Comput, vol.23, issue.6, pp.2095-2122, 2002. ,
Variational principles and free-boundary problems, 1988. ,
Numerical initial value problems in ordinary differential equations, 1971. ,
Solving ordinary differential equations. II, 1996. ,
Linear multistep method, vol.5, p.4591, 2010. ,
The primal-dual active set strategy as a semismooth Newton method, SIAM J. Optim, vol.13, issue.3, pp.865-888, 2002. ,
Variational inequalities and the pricing of American options, Acta Appl. Math, vol.21, issue.3, pp.263-289, 1990. ,
URL : https://hal.archives-ouvertes.fr/hal-01667008
On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems, Mathematical Models and Methods in Applied Sciences, vol.13, issue.05, pp.613-644, 2003. ,
Introduction to stochastic calculus applied to finance, Chapman & Hall/CRC Financial Mathematics Series, 2008. ,
TR-BDF2 for fast stable American option pricing, Journal of Computational Finance, vol.17, issue.3, pp.31-561, 2014. ,
Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications, Comm. Partial Differential Equations, vol.8, issue.10, pp.1101-1174, 1983. ,
Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II. Viscosity solutions and uniqueness, Comm. Partial Differential Equations, vol.8, issue.11, pp.1229-1276, 1983. ,
American option prices as unique viscosity solutions to degenerated Hamilton-Jacobi-Bellman equations, INRIA, 2000. ,
URL : https://hal.archives-ouvertes.fr/inria-00072718
On multigrid for linear complementarity problems with application to American-style options, Tenth Copper Mountain Conference on Multigrid Methods, vol.15, pp.165-185, 2001. ,
WENO and blended BDF discretizations for option pricing problems, Numerical mathematics and advanced applications, pp.419-428, 2003. ,
Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, J. Math. Systems Estim. Control, vol.8, issue.1, p.27, 1998. ,
The impact of a natural time change on the convergence of the Crank-Nicolson scheme, IMA J. Numer. Anal, vol.34, issue.3, pp.1156-1192, 2014. ,
A penalty scheme for monotone systems with interconnected obstacles: convergence and error estimates, 2018. ,
Uniform stability of a six-point scheme of higher order accuracy for the heat equation, ?. Vy?isl. Mat. i Mat. Fiz, vol.7, issue.1, pp.214-218, 1967. ,
Tools for computational finance, 2012. ,
Shout options: a framework for pricing contracts which can be modified by the investor, J. Comput. Appl. Math, vol.134, issue.1-2, pp.213-241, 2001. ,
Penalty methods for the solution of discrete HJB equations-continuous control and obstacle problems, SIAM J. Numer. Anal, vol.50, issue.2, pp.595-625, 2012. ,
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