Autore: Cinfrignini, Andrea
Titolo: Pricing through the choquet integral
Periodico: Annali del Dipartimento di metodi e modelli per l'economia, il territorio e la finanza
Anno: 2022 - Volume: 23 - Pagina iniziale: 1 - Pagina finale: 15

The classical no-arbitrage pricing theory allows to price assets through a linear pricing rule, byassuming a frictionless and competitive market. Moreover, completeness of the market assuresthat the pricing rule is defined as a discounted expected value with respect to a unique equivalentmartingale measure. On the other hand, under no-arbitrage assumption, incomplete models,such as the trinomial model, lead to a set of equivalent martingale measures. This suggeststo work with non-linear pricing rules that can allow frictions in the market. A generalizedpricing rule can be achieved by replacing additive measures with non-additive measures suchas convex capacities and belief functions in Dempster-Shafer theory. The paper recaps results onnon-additive measures and Choquet expectation as non-linear functional to be used in pricing.In the literature it has been proved that, under suitable conditions, a non-linear pricing rulecan be expressed as a Choquet expectation with respect to a convex capacity. In the trinomialmarket model the lower probability is a belief function, but it cannot be used to reach the lowerexpectation through the Choquet integral. Nevertheless it can avoid a generalized Dutch bookcondition in the framework of partially resolving uncertainty


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SICI: 2385-0825(2022)23<1:PTTCI>2.0.ZU;2-T
Testo completo: https://rosa.uniroma1.it/rosa02/annali_memotef/article/view/1392/1331

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