[1]
Adams R. A., Sobolev Spaces, Academic Press, New York, 1975.

[2]
Allegretto W., Lin Y. and Yang H., Finite element error estimates for a nonlocal problem in American option valuation, SIAM J. Numer. Anal., 39 (2001), pp. 834–857.

[3]
Amin K. and Khanna A., Convergence of American option values from discrete-to continuous-time financial models, Math. Finance, 4 (1994), pp. 289–304.

[4]
Barone-Adesi G. and Whaley R., Efficient Analytical Approximation of American Option Values, J. Fin., 42 (1987), pp. 301–320.

[5]
Badea L. and Wang J., A new formulation for the valuation of American options, I: Solution uniqueness, in Proceedings of the 19th Daewoo Workshop in Analysis and Scientific Computing, Park Eun-Jae and Lee Jongwoo, eds., 2000, pp. 3–16.

[6]
Badea L. and Wang J., A new formulation for the valuation of American options, II: Solution existence, in Proceedings of the 19th Daewoo Workshop in Analysis and Scientific Computing, Park Eun-Jae and Lee Jongwoo, eds., 2000, pp. 17–33.

[7]
Berenger J. P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), pp. 185–200.

[8]
Berenger J. P., Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 127 (1996), pp. 363–379.

[9]
Black F. and Scholes M., The pricing of options and corporate liabilities, J. Pol. Econ., 81 (1973), pp. 637–659.

[10]
Brennan M. and Schwartz E., The valuation of American put options, J. Fin., 32 (1977), pp. 449–462.

[11]
Brunner H., Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, 2004.

[12]
Carr P., Jarrow R. and Myneni R., Alternative characterizations of American put options, Math. Finance, 2 (1992), pp. 87–106.

[13]
Chen J., Wang D. S. and Wu H. J., An adaptive finite element method with a modified perfectly matched layer formulation for diffraction gratings, Commun. Comput. Phys., 6 (2009), pp. 290–318.

[14]
Chen Z. M. and Wu H. J., An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM. J. Numer. Anal., 41 (2003), pp. 799–826.

[15]
Chen Z. M., Guo B. Q. and Xiao Y. M., An hp adaptive uniaxial perfectly matched layer method for Helmholtz scattering problems, Commun. Comput. Phys., 5 (2009), pp. 546–564.

[16]
Ciarlet P. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.

[17]
Cox J. C., Ross S. A. and Rubinstein M., Option pricing: A simplified approach, J. Fin. Econ., 7 (1979), pp. 229–263.

[18]
Evans J. D., Kuske R. and Keller J. B., American options on assets with dividends near expiry, Math. Finance, 12 (2002), pp. 219–237.

[19]
Han H. and Wu X., A fast numerical method for the Black-Scholes equation of American options, SIAM J. Numer. Anal., 41 (2003), pp. 2081–2095.

[20]
Holmes A. D. and Yang H., A front-fixing finite element method for the valuation of American options, SIAM J. Sci. Comput., 30 (2008), pp. 2158–2180.

[21]
Hull J., Fundamentals of Futures and Options Markets, 6th Revised ed, Prentice Hall, Upper Saddle River, 2007.

[22]
Jaillet P., Lamberton D. and Lapeyre B., Variational inequalities and the pricing of American options, Acta Appl. Math., 21 (1990), pp. 263–289.

[23]
Ju N. and Zhong R., An Approximate Formula for Pricing American Options, The Journal of Derivatives, 7 (1999), pp. 31–40.

[24]
Jiang L., Mathematical Modeling and Methods of Option Pricing, World Scientific Press, Singapore, 2005.

[25]
Kim I. J., The analytic valuation of American puts, Rev. Fin. Stud., 3 (1990), pp. 547–572.

[26]
Kwok Y. K., Mathematical Models of Financial Derivatives, 2nd ed, Springer Finance, Berlin Heidelberg, 2008.

[27]
Lantos N. and Nataf F., Perfectly matched layers for the heat and advection-diffusion equations, J. Comput. Phys., 229 (2010), pp. 9042–9052

[28]
Lin Y. P., Zhang K. and Zou J., Studies on some perfectly matched layers for one-dimensional time-dependent systems, Adv. Comput. Math., 30 (2009), pp. 1–35.

[29]
Larsson S. and Thomee V., Partial Differential Equations with Numerical Methods, Springer-Verlag Press, Berlin Heidelberg, 2003.

[30]
Liang C. and Xiang X., Convergence of an anisotropic perfectly matched layer method for Helmholtz scattering problems, Numer. Math. Theory Methods Appl., 9 (2016), pp. 358–382.

[31]
Ma J., Xiang K. and Jiang Y., An integral equation method with high-order collocation implementations for pricing American put options, Int. J. Econ. Finance, 2 (2010), pp. 102–112.

[32]
Nicholls D. P. and Sward A., A discontinuous Galerkin method for pricing American options under the constant elasticity of variance model, Commun. Comput. Phys., 17 (2015), pp. 761–778.

[33]
Riviere B., Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation, SIAM. Frontiers in Applied Mathematics, 2008.

[34]
Schwartz E. S., The valuation of warrants: Implementing a new approach, J. Fin. Econ., 4 (1977), pp. 79–93.

[35]
Wu X. and Zheng W., An adaptive perfectly matched layer method for multiple cavity scattering problems, Commun. Comput. Phys., 19 (2016), pp. 534–558.

[36]
Zhang R., Song H. and Luan N., A weak Galerkin finite element method for the valuation of American options, Front. Math. China, 9 (2014), pp. 455–476.

[37]
Zhang K., Song H. and Li J., Front-fixing FEMs for the pricing of American options based on a PML technique, Appl. Anal., 94 (2015), pp. 903–931.