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NO‐FREE‐LUNCH EQUIVALENCES FOR EXPONENTIAL LÉVY MODELS UNDER CONVEX CONSTRAINTS ON INVESTMENT
Author(s) -
Kardaras Constantinos
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00363.x
Subject(s) - semimartingale , equivalence (formal languages) , mathematical economics , lévy process , portfolio , exponential function , regular polygon , asset (computer security) , economics , financial market , financial modeling , mathematics , computer science , finance , pure mathematics , mathematical analysis , geometry , computer security
We provide equivalence of numerous no‐free‐lunch type conditions for financial markets where the asset prices are modeled as exponential Lévy 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 wealth. Furthermore, we connect the previous to the existence of the numéraire portfolio , both for its particular expositional clarity in exponential Lévy models and as a first step in obtaining analogues of the no‐free‐lunch equivalences in general semimartingale models, a task that is taken on in Karatzas and Kardaras (2007).