We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing–hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang–Morton–Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure.In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.

Pointwise Arbitrage Pricing Theory in Discrete Time / M. Burzoni, M. Frittelli, Z. Hou, M. Maggis, J. Obłój. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 44:3(2019 Aug), pp. 1034-1057. [10.1287/moor.2018.0956]

Pointwise Arbitrage Pricing Theory in Discrete Time

M. Burzoni
Primo
;
M. Frittelli
Secondo
;
M. Maggis
Penultimo
;
2019-08

Abstract

We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing–hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang–Morton–Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure.In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.
robust modelling approach; fundamental theorem of asset pricing; superhedging duality; semistatic optimization; pointwise stochastic analysis; arbitrage pricing theory; model ambiguity; Knightian uncertainty
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/06 - Probabilita' e Statistica Matematica
3-apr-2019
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/636817
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