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Properly discounted asset prices are semimartingales

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Abstract

We study general undiscounted asset price processes, which are only assumed to be nonnegative, adapted and RCLL (but not a priori semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage, the original prices discounted by the value process of any simple strategy with positive wealth must follow semimartingales. We also establish a corresponding version of the fundamental theorem of asset pricing that involves supermartingale discounters with an additional strict positivity property.

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Acknowledgements

We gratefully acknowledge financial support by the ETH Foundation via the Stochastic Finance Group (SFG) at ETH Zurich and by the Swiss Finance Institute (SFI). The first author thanks Matteo Burzoni for discussions, questions and general support. We also thank two anonymous referees and an Associate Editor for critical comments that led us to rewrite our paper and explain our contribution more clearly.

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  1. Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland

    Dániel Ágoston Bálint & Martin Schweizer

  2. Swiss Finance Institute, Walchestrasse 9, 8006, Zurich, Switzerland

    Martin Schweizer

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  1. Dániel Ágoston Bálint
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  2. Martin Schweizer
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Correspondence to Martin Schweizer.

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Bálint, D.Á., Schweizer, M. Properly discounted asset prices are semimartingales. Math Finan Econ 14, 661–674 (2020). https://doi.org/10.1007/s11579-020-00269-8

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  • DOI: https://doi.org/10.1007/s11579-020-00269-8

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