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Absence of arbitrage in a general framework

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  • Hasanjan Sayit

Abstract

Cheridito (Finance Stoch 7:533–553, 2003 ) studies a financial market that consists of a money market account and a risky asset driven by a fractional Brownian motion. It is shown that arbitrage possibilities in such markets can be excluded by suitably restricting the class of allowable trading strategies. In this note, we show an analogous result in a multi-asset market where the discounted risky asset prices follow more general non-semimartingale models. In our framework, investors are allowed to trade between a risk-free asset and multiple risky assets by following simple trading strategies that require a minimal deterministic waiting time between any two trading dates. We present a condition on the discounted risky asset prices that guarantee absence of arbitrage in this setting. We give examples that satisfy our condition and study its invariance under certain transformations. Copyright Springer-Verlag 2013

Suggested Citation

  • Hasanjan Sayit, 2013. "Absence of arbitrage in a general framework," Annals of Finance, Springer, vol. 9(4), pages 611-624, November.
    • Handle: RePEc:kap:annfin:v:9:y:2013:i:4:p:611-624
    DOI: 10.1007/s10436-012-0207-0
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    References listed on IDEAS

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    1. Erhan Bayraktar & Hasanjan Sayit, 2010. "No arbitrage conditions for simple trading strategies," Annals of Finance, Springer, vol. 6(1), pages 147-156, January.
    2. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    5. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    6. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    7. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    8. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    9. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
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    Cited by:

    1. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Annals of Finance, Springer, vol. 19(2), pages 141-168, June.
    2. Takaki Hayashi & Yuta Koike, 2017. "No arbitrage and lead-lag relationships," Papers 1712.09854, arXiv.org.
    3. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Post-Print hal-03284660, HAL.
    4. Hayashi, Takaki & Koike, Yuta, 2019. "No arbitrage and lead–lag relationships," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    5. Dorsaf Cherif & Emmanuel Lépinette, 2021. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Working Papers hal-03284660, HAL.

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    More about this item

    Keywords

    Simple trading strategies; Absence of arbitrage; Conditional full support; Non-semimartingale models; G10;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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