On the Numerical Solution of Some Non-Linear Stochastic Differential Equations Using the Semi-Discrete Method
| Autor: | Nikolaos Halidias, Ioannis S. Stamatiou |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Applied Mathematics Hölder condition Discrete method Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Stochastic differential equation Rate of convergence FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| Zdroj: | Computational Methods in Applied Mathematics. 16:105-132 |
| ISSN: | 1609-9389 1609-4840 |
| DOI: | 10.1515/cmam-2015-0028 |
| Popis: | We are interested in the numerical solution of stochastic differential equations with non-negative solutions. Our goal is to construct explicit numerical schemes that preserve positivity, even for super-linear stochastic differential equations. It is well known that the usual Euler scheme diverges on super-linear problems and the tamed Euler method does not preserve positivity. In that direction, we use the semi-discrete method that the first author has proposed in two previous papers. We propose a new numerical scheme for a class of stochastic differential equations which are super-linear with non-negative solution. The Heston 3/2-model appearing in financial mathematics belongs to this class of stochastic differential equations. For this model we prove, through numerical experiments, the “optimal” order of strong convergence at least 1/2 of the semi-discrete method. |
| Databáze: | OpenAIRE |
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