Risk-hedging a European option with a convex risk measure and without no-arbitrage condition

In this article, we revisit the discrete-time problem of pricing a contingent claim with respect to a dynamic risk measure defined by its acceptance sets. Without any no-arbitrage condition, we show that it is possible to characterize the prices of a European claim. Our analysis reveals a natural we...

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2023-01, Vol.95 (1), p.118-155
Main Authors: Lepinette, Emmanuel, Zhao, Jun
Format: Article
Language:English
Subjects:
absence of instantaneous profit aip
conditional essential infimum and supremum
dynamic risk measures
random sets
Risk
Risk-hedging prices
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Summary:In this article, we revisit the discrete-time problem of pricing a contingent claim with respect to a dynamic risk measure defined by its acceptance sets. Without any no-arbitrage condition, we show that it is possible to characterize the prices of a European claim. Our analysis reveals a natural weak no-arbitrage condition that we study. This is a condition formulated in terms of the (risk) hedging prices instead of the attainable claims. Our approach is not based on a robust representation of the risk measure and we do not suppose the existence of a risk-neutral probability measure.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2022.2055966