Pricing through the Choquet integral
The classical no-arbitrage pricing theory allows to price assets through a linear pricing rule, by assuming a frictionless and competitive market. Moreover, completeness of the market assures that the pricing rule is defined as a discounted expected value with respect to a unique equivalent martingale 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 suggests to work with non-linear pricing rules that can allow frictions in the market. A generalized pricing rule can be achieved by rep... Mehr ...
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Dokumenttyp: | Artikel |
Erscheinungsdatum: | 2022 |
Verlag/Hrsg.: |
Sapienza Università di Roma
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Schlagwörter: | incomplete market / lower pricing rule / trinomial model / non-additive measure / Choquet integral / belief function / generalized no-Dutch book |
Sprache: | Englisch |
Permalink: | https://search.fid-benelux.de/Record/base-26677034 |
Datenquelle: | BASE; Originalkatalog |
Powered By: | BASE |
Link(s) : | https://hdl.handle.net/11573/1628425 |
The classical no-arbitrage pricing theory allows to price assets through a linear pricing rule, by assuming a frictionless and competitive market. Moreover, completeness of the market assures that the pricing rule is defined as a discounted expected value with respect to a unique equivalent martingale 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 suggests to work with non-linear pricing rules that can allow frictions in the market. A generalized pricing rule can be achieved by replacing additive measures with non-additive measures such as convex capacities and belief functions in Dempster-Shafer theory. The paper recaps results on non-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 rule can be expressed as a Choquet expectation with respect to a convex capacity. In the trinomial market model the lower probability is a belief function, but it cannot be used to reach the lower expectation through the Choquet integral. Nevertheless it can avoid a generalized Dutch book condition in the framework of partially resolving uncertainty.