On construction of boundary preserving numerical schemes
arXiv:1601.078643 citationsh-index: 11
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This work provides an incremental improvement in numerical methods for stochastic differential equations with boundary constraints, relevant to computational finance and applied mathematics.
The paper extends the semi-discrete technique with a split-step method to construct an explicit, positivity-preserving numerical scheme for the Ait-Sahalia model. The scheme maintains boundary preservation, though no concrete numerical results are provided.
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.