Dynamic bid–ask pricing under Dempster-Shafer uncertainty

• Published in: Journal of mathematical economics Vol. 107; p. 102871
• Main Authors: Cinfrignini, Andrea, Petturiti, Davide, Vantaggi, Barbara
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2023
• Subjects: Belief function; Bid–ask spread; Dynamic pricing rule; Time-homogeneous Markov multiplicative binomial process; Dynamic pricing rule; Bid–ask spread; Time-homogeneous Markov multiplicative binomial process; Belief function
• ISSN: 0304-4068; 1873-1538
• DOI: 10.1016/j.jmateco.2023.102871

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.