Strict Local Martingales Via Filtration Enlargement

Electronic version of an article published as [International Journal of Theoretical and Applied Finance, Volume 23, Number 1, 2020, 28 pages] [DOI/10.1142/S0219024920500016] © [copyright World Scientific Publishing Company]

Posted: 1 Feb 2021

See all articles by Aditi Dandapani

Aditi Dandapani

University of Zurich, Institute of Mathematics, Department of Banking and Finance, University of Zurich, Institute of Mathematics, Department of Banking and Finance, Students

Philip Protter

Columbia University

Date Written: December 27, 2019

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: Strict local martingales, filtration expansion, bubbles

JEL Classification: G12, G19

Suggested Citation

Dandapani, Aditi and Protter, Philip, Strict Local Martingales Via Filtration Enlargement (December 27, 2019). Electronic version of an article published as [International Journal of Theoretical and Applied Finance, Volume 23, Number 1, 2020, 28 pages] [DOI/10.1142/S0219024920500016] © [copyright World Scientific Publishing Company] , Available at SSRN: https://ssrn.com/abstract=3663037

Aditi Dandapani

University of Zurich, Institute of Mathematics, Department of Banking and Finance, University of Zurich, Institute of Mathematics, Department of Banking and Finance, Students ( email )

Switzerland

Philip Protter (Contact Author)

Columbia University ( email )

Mail Code 4403
New York, NY 10027
United States
2128511245 (Phone)
2128512164 (Fax)

HOME PAGE: http://www.stat.columbia.edu/~protter/

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