We deal with the problem of pricing in a multi-period binomial market model, allowing for frictions in the form of bid–ask spreads. We introduce and characterize time-homogeneous Markov multiplicative binomial processes under Dempster-Shafer uncertainty together with the induced conditional Choquet expectation operator. Given a market formed by a frictionless risk-free bond and a non-dividend paying stock with frictions, we prove the existence of an equivalent one-step Choquet martingale belief function. We then propose a dynamic Choquet pricing rule with bid–ask spreads showing that the discounted lower price process of a European derivative contract on the stock is a Choquet super-martingale. We finally provide a normative justification in terms of a dynamic generalized no-arbitrage condition relying on the notion of partially resolving uncertainty due to Jaffray.

Dynamic bid–ask pricing under Dempster-Shafer uncertainty / Cinfrignini, A.; Petturiti, D.; Vantaggi, B.. - In: JOURNAL OF MATHEMATICAL ECONOMICS. - ISSN 0304-4068. - 107:(2023). [10.1016/j.jmateco.2023.102871]

Dynamic bid–ask pricing under Dempster-Shafer uncertainty

Cinfrignini A.;Vantaggi B.
2023

Abstract

We deal with the problem of pricing in a multi-period binomial market model, allowing for frictions in the form of bid–ask spreads. We introduce and characterize time-homogeneous Markov multiplicative binomial processes under Dempster-Shafer uncertainty together with the induced conditional Choquet expectation operator. Given a market formed by a frictionless risk-free bond and a non-dividend paying stock with frictions, we prove the existence of an equivalent one-step Choquet martingale belief function. We then propose a dynamic Choquet pricing rule with bid–ask spreads showing that the discounted lower price process of a European derivative contract on the stock is a Choquet super-martingale. We finally provide a normative justification in terms of a dynamic generalized no-arbitrage condition relying on the notion of partially resolving uncertainty due to Jaffray.
2023
Belief function; Bid–ask spread; Dynamic pricing rule; Time-homogeneous Markov multiplicative binomial process
01 Pubblicazione su rivista::01a Articolo in rivista
Dynamic bid–ask pricing under Dempster-Shafer uncertainty / Cinfrignini, A.; Petturiti, D.; Vantaggi, B.. - In: JOURNAL OF MATHEMATICAL ECONOMICS. - ISSN 0304-4068. - 107:(2023). [10.1016/j.jmateco.2023.102871]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1685779
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