Uniform Integrability of a Single Jump Local Martingale with State-Dependent Characteristics

Michael Schatz and Didier Sornette
Additional contact information
Michael Schatz: ETH Zurich
Didier Sornette: ETH Zürich and Swiss Finance Institute

No 17-21, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We investigate a deterministic criterion to determine whether a diffusive local martingale with a single jump and state-dependent characteristics is a uniformly integrable martingale. We allow the diffusion coefficient, the jump hazard rate and the relative jump size to depend on the state and prove that the process is a uniformly integrable martingale if and only if the relative jump size is bounded away from one and the hazard rate is large enough compared to the diffusion component. The result helps to classify seemingly explosive behaviour in diffusive local martingales compensated by the existence of a jump. Moreover, processes of this type can be used to model financial bubbles in stock prices as deviation from the fundamental value. We present a simple framework to illustrate this application.

Keywords: Uniformly Integrable Martingales; Local Martingales; Single Jump; Explosive Diffusion Processes; Financial Bubbles (search for similar items in EconPapers)
JEL-codes: C60 G01 G10 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2017-06
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2987695 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1721

Access Statistics for this paper

More papers in Swiss Finance Institute Research Paper Series from Swiss Finance Institute Contact information at EDIRC.
Bibliographic data for series maintained by Ridima Mittal ().