Scaling limits of processes with fast nonlinear mean reversion

Thomas Cayé, Martin Herdegen and Johannes Muhle-Karbe

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 1994-2031

Abstract: We derive scaling limits for integral functionals of Itô processes with fast nonlinear mean-reversion speeds. In these limits, the fast mean-reverting process is “averaged out” by integrating against its invariant measure. The convergence is uniformly in probability and, under mild integrability conditions, also in Sp. These results 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 [11].

Keywords: Processes with fast nonlinear mean reversion; Scaling limits (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.06.008

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