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- Title
Numerical solutions of Black-Scholes integro-differential equations with convergence analysis.
- Authors
RIVAZ, Azim; MOHSENI MOGHADAM, Mahmoud; BANI ASADI, Samaneh
- Abstract
Stochastic integro-differential equations are obtained when we consider prices jump in financial modelling. In this paper, these equations are solved numerically by applying the two-dimensional Tau method with ordinary bases. Next, the numerical solutions of the equations above are investigated by the ordinary bases to the Hermitian one. Moreover, we provide an error analysis for the Tau method with ordinary bases. Also, we will prove that the errors of the approximate solutions decay exponentially in weighted L² -norm. At the end, we will provide some numerical examples which show the efficiency and accuracy of the method.
- Subjects
NUMERICAL solutions to integro-differential equations; NUMERICAL solutions to equations; INTEGRO-differential equations; HERMITIAN forms; ERROR analysis in mathematics; JUMP processes
- Publication
Turkish Journal of Mathematics, 2019, Vol 43, Issue 3, p1080
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1812-89