The Annals of Applied Probability

A theoretical framework for the pricing of contingent claims in the presence of model uncertainty

Laurent Denis and Claude Martini

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Abstract

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. We obtain a partial characterization result and a full characterization which extends Avellaneda, Levy and Paras results in the UVM case.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 2 (2006), 827-852.

Dates
First available in Project Euclid: 29 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1151592252

Digital Object Identifier
doi:10.1214/105051606000000169

Mathematical Reviews number (MathSciNet)
MR2244434

Zentralblatt MATH identifier
1142.91034

Subjects
Primary: 60H05: Stochastic integrals 60G44: Martingales with continuous parameter
Secondary: 31C15: Potentials and capacities

Keywords
Superreplication capacity uncertain volatility model nondominated model stochastic integral option pricing

Citation

Denis, Laurent; Martini, Claude. A theoretical framework for the pricing of contingent claims in the presence of model uncertainty. Ann. Appl. Probab. 16 (2006), no. 2, 827--852. doi:10.1214/105051606000000169. https://projecteuclid.org/euclid.aoap/1151592252


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