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Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 65M06, 65M12.The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order accuracy....

Non-topological condensates in self-dual Chern-Simons gauge theory

Takashi Suzuki, Futoshi Takahashi (2004)

Banach Center Publications

This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.

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