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Trajectory Based Models, Arbitrage and Continuity

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  • Alexander Alvarez
  • Sebastian Ferrando

Abstract

The paper develops no arbitrage results for trajectory based models by imposing general constraints on the trading portfolios. The main condition imposed, in order to avoid arbitrage opportunities, is a local continuity requirement on the final portfolio value considered as a functional on the trajectory space. The paper shows this to be a natural requirement by proving that a large class of practical trading strategies, defined by means of trajectory based stopping times, give rise to locally continuous functionals. The theory is illustrated, with some detail, for two specific trajectory models of practical interest. The implications for stochastic models which are not semimartingales are described. The present paper extends some of the results in [1] by incorporating in the formalism a larger set of trading portfolios.

Suggested Citation

  • Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    • Handle: RePEc:arx:papers:1403.5685
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    References listed on IDEAS

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    1. Boshuizen, Frans A. & Hill, T. P., 1992. "Moment-based minimax stopping functions for sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 303-316, December.
    2. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    3. 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.
    4. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
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    Cited by:

    1. Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769, arXiv.org, revised Nov 2015.

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