ANDREA CINFRIGNINI

Dottore di ricerca

ciclo: XXXV



Titolo della tesi: Discrete time models for bid-ask pricing under Dempster-Shafer uncertainty

As is well-known, real financial markets depart from simplifying hypotheses of classical no-arbitrage pricing theory. In particular, they show the presence of frictions in the form of bid-ask spread. For this reason, the aim of the thesis is to provide a model able to manage these situations, relying on a non-linear pricing rule defined as (discounted) Choquet integral with respect to a belief function. Under the partially resolving uncertainty principle, we generalize the first fundamental theorem of asset pricing in the context of belief functions. Furthermore, we show that a generalized arbitrage-free lower pricing rule can be characterized as a (discounted) Choquet expectation with respect to an equivalent inner approximating (one-step) Choquet martingale belief function. Then, we generalize the Choquet pricing rule dinamically: we characterize a reference belief function such that a multiplicative binomial process satisfies a suitable version of time-homogeneity and Markov properties and we derive the induced conditional Choquet expectation operator. In a multi-period market with a risky asset admitting bid-ask spread, we assume that its lower price process is modeled by the proposed time-homogeneous Markov multiplicative binomial process. Here, we generalize the theorem of change of measure, proving the existence of an equivalent one-step Choquet martingale belief function. Then, we prove that the (discounted) lower price process of a European derivative is a one-step Choquet martingale and a k-step Choquet super-martingale, for k >= 2.

Produzione scientifica

11573/1685779 - 2023 - Dynamic bid–ask pricing under Dempster-Shafer uncertainty
Cinfrignini, A.; Petturiti, D.; Vantaggi, B. - 01a Articolo in rivista
rivista: JOURNAL OF MATHEMATICAL ECONOMICS (-Amsterdam Netherlands: Elsevier BV -Amsterdam : North-Holland Publ. Co.) pp. - - issn: 0304-4068 - wos: WOS:001046921300001 (1) - scopus: 2-s2.0-85165266601 (1)

11573/1666261 - 2023 - Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting
Cinfrignini, Andrea; Petturiti, Davide; Vantaggi, Barbara - 01a Articolo in rivista
rivista: ANNALS OF OPERATIONS RESEARCH (Switzerland: Springer Nature Dordrecht: Kluwer Academic Publishers. Amsterdam; Bussum: Baltzer Science Publishers.) pp. 103-137 - issn: 0254-5330 - wos: WOS:000900814000001 (5) - scopus: 2-s2.0-85144230970 (6)

11573/1628425 - 2022 - Pricing through the Choquet integral
Cinfrignini, Andrea - 01a Articolo in rivista
rivista: ANNALI DEL DIPARTIMENTO DI METODI E MODELLI PER L'ECONOMIA, IL TERRITORIO E LA FINANZA ... (Roma: Sapienza Università editrice, 2017- Bologna: Patron, 2012-2014) pp. - - issn: 2611-6634 - wos: (0) - scopus: (0)

11573/1560233 - 2022 - Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting
Cinfrignini, Andrea; Petturiti, Davide; Vantaggi, Barbara - 06a Curatela

11573/1650092 - 2022 - Markov and Time-Homogeneity Properties in Dempster-Shafer Random Walks
Cinfrignini, Andrea; Petturiti, Davide; Vantaggi, Barbara - 02a Capitolo o Articolo
libro: Information Processing and Management of Uncertainty in Knowledge-Based Systems - (978-3-031-08970-1; 978-3-031-08971-8)

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