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Some Remarks On Arbitrage And Preferences In Securities Market Models

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  • Marco Frittelli

Abstract

We introduce the notion of a market‐free‐lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize no arbitrage (NA) and no‐free‐lunch‐with‐vanishing‐risk (NFLVR) in terms of the market‐free‐lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, respectively monotone and continuous, utility functions that determines the absence of the market‐free‐lunch. We also provide a direct proof of the equivalence between the absence of a market‐free‐lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure.

Suggested Citation

  • Marco Frittelli, 2004. "Some Remarks On Arbitrage And Preferences In Securities Market Models," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 351-357, July.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:3:p:351-357
    DOI: 10.1111/j.0960-1627.2004.00194.x
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    Cited by:

    1. Rossello, Damiano, 2012. "Arbitrage in skew Brownian motion models," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 50-56.
    2. Badics, Tamás, 2011. "Az arbitrázs preferenciákkal történő karakterizációjáról [On the characterization of arbitrage in terms of preferences]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 727-742.
    3. Claudio Fontana & Bernt Øksendal & Agnès Sulem, 2015. "Market Viability and Martingale Measures under Partial Information," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 15-39, March.

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