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Finance and Stochastics

07.09.2018

Weak time-derivatives and no-arbitrage pricing

verfasst von: Massimo Marinacci, Federico Severino

Erschienen in: Finance and Stochastics | Ausgabe 4/2018

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Abstract

We prove a risk-neutral pricing formula for a large class of semimartingale processes through a novel notion of weak time-differentiability that permits to differentiate adapted processes. In particular, the weak time-derivative isolates drifts of semimartingales and is null for martingales. Weak time-differentiability enables us to characterize no-arbitrage prices as solutions of differential equations, where interest rates play a key role. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (Econometrica 77:177–234, 2009) by employing weak time-derivatives.

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Titel: Weak time-derivatives and no-arbitrage pricing
verfasst von: Massimo Marinacci
Federico Severino
Publikationsdatum: 07.09.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Finance and Stochastics / Ausgabe 4/2018
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-018-0371-9