No-Free-Lunch equivalences for exponential Levy models

TL;DR

This paper establishes the equivalence of various no-free-lunch conditions in exponential Levy models, showing that any arbitrage opportunity implies significant wealth gains, and connects these conditions to the existence of the numeraire portfolio.

Contribution

It demonstrates the equivalence of no-free-lunch conditions in exponential Levy models and links these to the existence of the numeraire portfolio, advancing understanding in mathematical finance.

Findings

No-free-lunch conditions are equivalent in exponential Levy models.

Any free lunch leads to unbounded wealth growth.

Connection established between no-free-lunch conditions and the numeraire portfolio.

Abstract

We provide equivalence of numerous no-free-lunch type conditions for financial markets where the asset prices are modeled as exponential Levy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to be of the most egregious type, generating an increasing ealth. Furthermore, we connect the previous to the existence of the numeraire portfolio, both for its particular expositional clarity in exponential Levy models and as a first step in obtaining analogues of the no-free-lunch equivalences in general semimartingale models.