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No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment

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  • Constantinos Kardaras

Abstract

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).

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  • Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:2:p:161-187
    DOI: 10.1111/j.1467-9965.2009.00363.x
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    References listed on IDEAS

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    1. Lucien Foldes, 1991. "Optimal Sure Portfolio Plans," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 15-55, April.
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    5. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
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    Cited by:

    1. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    2. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    3. Carla Mereu & Robert Stelzer, 2015. "A BSDE arising in an exponential utility maximization problem in a pure jump market model," Papers 1508.07561, arXiv.org, revised Jan 2016.
    4. Claudio Fontana, 2013. "A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing," Papers 1311.7027, arXiv.org.
    5. Johannes Temme, 2012. "Power utility maximization in exponential Lévy models: convergence of discrete-time to continuous-time maximizers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 21-41, August.
    6. Jacopo Mancin & Wolfgang J. Runggaldier, 2015. "On the Existence of Martingale Measures in Jump Diffusion Market Models," Papers 1511.08349, arXiv.org.
    7. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.

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