  his paper presents finite element methods for solving numerically the
Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model for option pricing
with transaction costs. Spatial finite element models based on P1 and/or P2
elements are formulated using some group finite elements and numerical
quadrature to handle the nonlinear term, in combination with a
Crank-Nicolson-type temporal scheme. The temporal scheme is implemented using
the Rannacher approach. Spatial-temporal mesh-size ratios are observed for
controlling the stability of our method. Our results compare favorably with the
finite difference results in the literature for the model.
