No arbitrage in continuous financial markets

Artikel

We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Itô process or a positive diffusion with Markov switching. In particular, we derive conditions for the existence of the minimal martingale measure. We also show that for Markov switching models the minimal martingale measure preserves the independence of the noise and we study how the minimal martingale measure can be modified to change the structure of the switching mechanism. Our main mathematical tools are new criteria for the martingale and strict local martingale property of certain stochastic exponentials.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Mathematics and Financial Economics ; ISSN: 1862-9660 ; Volume: 14 ; Year: 2020 ; Issue: 3 ; Pages: 461-506 ; Berlin, Heidelberg: Springer

Classification and Topics

• Classification: Wirtschaft ; Structure and Scope of Government: General ; Mathematical Methods ; General Financial Markets: Other
• Subject: No arbitrage ; Financial bubble ; Minimal martingale measure ; Itô process ; Switching diffusion ; Stochastic exponential

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Criens, David
• Event: Veröffentlichung
• (who): Springer
• (where): Berlin, Heidelberg
• (when): 2020

Further information

• DOI: doi:10.1007/s11579-020-00262-1
• Last update: 10.03.2025, 11:45 AM CET