• Corpus ID: 214743252

# The Heston stochastic volatility model has a boundary trace at zero volatility.

@article{Alziary2020TheHS,
title={The Heston stochastic volatility model has a boundary trace at zero volatility.},
author={B'en'edicte Alziary and Peter Tak'avc},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Published 1 April 2020
• Mathematics
• arXiv: Analysis of PDEs
We establish boundary regularity results in H\"older spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up in the spatial domain (upper half-plane) $\mathbb{H} = \mathbb{R}\times (0,\infty)\subset \mathbb{R}^2$. Starting with nonsmooth initial data $u_0\in H$, we take advantage of smoothing properties of the parabolic semigroup $\mathrm{e}^{-t\mathcal{A}}\colon H\to H$, $t\in \mathbb{R}_+$, generated by the Heston model…
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