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arXiv · 1710.11202

Scaling Limits of Processes with Fast Nonlinear Mean Reversion

Thomas Cayé·Martin Herdegen·Johannes Muhle-Karbe
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Abstract

We derive scaling limits for integral functionals of It\^o processes with fast nonlinear mean-reversion speed. We show that in these limits, the fast mean-reverting process is "averaged out" by integrating against its invariant measure. These convergence results hold uniformly in probability and, under mild integrability conditions, also in $\mathcal{S}^p$. They are a crucial building block for the analysis of portfolio choice models with small superlinear transaction costs, carried out in the companion paper of the present study.

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Thomas Cayé, Martin Herdegen, Johannes Muhle-Karbe. 2017-10-30. Scaling Limits of Processes with Fast Nonlinear Mean Reversion. https://arxiv.org/abs/1710.11202

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