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STRICT LOCAL MARTINGALES VIA FILTRATION ENLARGEMENT

ADITI DANDAPANI

Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

E-mail Address: ad2259@caa.columbia.edu

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and

PHILIP PROTTER

http://orcid.org/0000-0003-1344-0403

Statistics Department, Columbia University, New York, NY 10027, USA

E-mail Address: pep2117@columbia.edu

Corresponding author.

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https://doi.org/10.1142/S0219024920500016Cited by:0 (Source: Crossref)

Abstract

A strict local martingale is a local martingale that is not a martingale. We investigate how such a process might arise from a true martingale as a result of an enlargement of the filtration and a change of measure. We study and implement a particular type of enlargement, initial expansion of filtration, for stochastic volatility models with and without jumps and provide sufficient conditions in each of these cases such that initial expansion can create a strict local martingale. We provide examples of initial enlargement that effect this change.

Keywords:

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