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High-order compact finite difference schemes for a nonlinear Black-Scholes equation. (English) Zbl 1070.91024
Summary: A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of {\it A. Rigal} [J. Comp. Phys. 114, No. 1, 59--76 (1994; Zbl 0807.65096)], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

MSC:
91B28Finance etc. (MSC2000)
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
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