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Far field boundary conditions for Black-Scholes equations. (English) Zbl 0990.35013
The partial differential equations approach for valuing European-style options is considered. In order to solve the equations numerically by finite difference or finite element methods it is necessary to introduce an artificial boundary in order to make the computational domain bounded. Pointwise bounds for the error cause by various boundary conditions imposed on the artificial boundary are derived. The error estimates can be used to determine a priori a suitable location for the artificial boundary in terms of a given error tolerance.

MSC:
35A35 Theoretical approximation in context of PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
91B99 Mathematical economics
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