QUADRATIC CONVERGENCE OF A PENALTY METHOD FOR VALUING AMERICAN OPTIONS

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Analysis of a penalty method for pricing a guaranteed minimum withdrawal benefit (GMWB) (2012, background): “This issue is also discussed in Forsyth and Vetzal (2002).559 6.4 Comparison: Penalty Method (Singular Control) and Impulse Control560 As outlined in (Zakamouline, 2005), it is almost always possible to formulate a singular control561 problem as an impulse control problem, with arbitrarily small…”
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance (2007, methodology): “A numerical algorithm based on the penalty method is described in [22].”
Robust numerical valuation of European and American options under the CGMY process (2007, methodology): “The value of Large is chosen depending on the accuracy desired (see [26]).”
Robust numerical methods for contingent claims under jump diffusion processes (2005, methodology): “As mentioned in Section 6, this is easily handled in our framework by combining the fixed point iteration with the penalty method described in Forsyth and Vetzal (2002).”