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

Andrea Cinfrignini (), Davide Petturiti () and Barbara Vantaggi
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Andrea Cinfrignini: Department MEMOTEF, La Sapienza University of Rome
Davide Petturiti: University of Perugia

Annals of Operations Research, 2023, vol. 321, issue 1, No 5, 103-137

Abstract: 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.

Keywords: Equivalent martingale measures; Belief functions; Generalized no-arbitrage principle; Lower pricing rule (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-05126-z

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