Generalized statistical arbitrage concepts and related gain strategies

Christian Rein, Ludger Rüschendorf and Thorsten Schmidt

Mathematical Finance, 2021, vol. 31, issue 2, 563-594

Abstract: The notion of statistical arbitrage introduced in Bondarenko (2003) is generalized to statistical G‐arbitrage corresponding to trading strategies which yield positive gains on average in a class of scenarios described by a σ‐algebra G. This notion contains classical arbitrage as a special case. Admitting general static payoffs as generalized strategies, as done in Kassberger and Liebmann (2017) in the case of one pricing measure, leads to the notion of generalized statistical G‐arbitrage. We show that even under standard no‐arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we prove that the characterization in Bondarenko (2003), no statistical arbitrage being equivalent to the existence of an equivalent local martingale measure with a path‐independent density, is not correct in general. We establish that this equivalence holds true in complete markets and we derive a general sufficient condition for statistical G‐arbitrages. As a main result we derive the equivalence of no statistical G‐arbitrage to no generalized statistical G‐arbitrage. In the second part of the paper we construct several classes of profitable generalized strategies with respect to various choices of the σ‐algebra G. In particular, we consider several forms of embedded binomial strategies and follow‐the‐trend strategies as well as partition‐type strategies. We study and compare their behavior on simulated data and also evaluate their performance on market data.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://doi.org/10.1111/mafi.12300

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:bla:mathfi:v:31:y:2021:i:2:p:563-594

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().