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Trajectory-Based Models, Arbitrage And Continuity

Author

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  • ALEXANDER ALVAREZ

    (Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON M5B 2K3, Canada)

  • SEBASTIAN E. FERRANDO

    (Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON M5B 2K3, Canada)

Abstract

In a nonprobabilistic setting, we prove general trajectory-based models to have no free lunch with vanishing risk. The main ingredient is a local continuity requirement on the final portfolio value considered as a functional on the trajectory space. This is shown to be a natural assumption by establishing 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 applied to two specific trajectory models of practical interest. The established results are then used to derive no free lunch results for nonsemimartingale stochastic models.

Suggested Citation

  • Alexander Alvarez & Sebastian E. Ferrando, 2016. "Trajectory-Based Models, Arbitrage And Continuity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-34, May.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:03:n:s0219024916500151
    DOI: 10.1142/S0219024916500151
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    References listed on IDEAS

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