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Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting

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  • Andrea Cinfrignini

    (Department MEMOTEF, La Sapienza University of Rome)

  • Davide Petturiti

    (University of Perugia)

  • Barbara Vantaggi

    (Department MEMOTEF, La Sapienza University of Rome)

Abstract

We consider a one-period market model composed by a risk-free asset and a risky asset with n possible future values (namely, a n-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in such market model, showing that it is a belief function. Then, we reformulate a general one-period pricing problem in the framework of belief functions: this allows to model frictions in the market and can be justified in terms of partially resolving uncertainty according to Jaffray. We provide a generalized no-arbitrage condition for a generic one-period market model under partially resolving uncertainty and show that the “risk-neutral” belief function arising in the one-period n-nomial market model does not allow to satisfy such condition. Finally, we derive a generalized arbitrage-free lower pricing rule through an inner approximation of the “risk-neutral” belief function arising in the one-period n-nomial market model.

Suggested Citation

  • Andrea Cinfrignini & Davide Petturiti & Barbara Vantaggi, 2023. "Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting," Annals of Operations Research, Springer, vol. 321(1), pages 103-137, February.
    • Handle: RePEc:spr:annopr:v:321:y:2023:i:1:d:10.1007_s10479-022-05126-z
    DOI: 10.1007/s10479-022-05126-z
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    Cited by:

    1. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).

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