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Weak and strong no-arbitrage conditions for continuous financial markets

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  • Claudio Fontana

Abstract

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results.

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  • Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers 1302.7192, arXiv.org, revised May 2014.
    • Handle: RePEc:arx:papers:1302.7192
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    References listed on IDEAS

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    1. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    2. Eva Strasser, 2005. "Characterization of arbitrage-free markets," Papers math/0503473, arXiv.org.
    3. Tahir Choulli & Jun Deng & Junfeng Ma, 2012. "How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related," Papers 1211.4598, arXiv.org, revised Jun 2014.
    4. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..
    5. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    6. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    9. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
    10. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    11. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    12. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    13. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    15. Dzhaparidze, Kacha & Spreij, Peter, 1993. "On correlation calculus for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 283-299, June.
    16. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    17. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    18. Cheng, Susan T., 1991. "On the feasibility of arbitrage-based option pricing when stochastic bond price processes are involved," Journal of Economic Theory, Elsevier, vol. 53(1), pages 185-198, February.
    19. Jarrow, Robert & Protter, Philip, 2005. "Large traders, hidden arbitrage, and complete markets," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2803-2820, November.
    20. Gianluca Cassese, 2005. "A Note On Asset Bubbles In Continuous-Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 523-536.
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    Cited by:

    1. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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