Abstract
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.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 This means that the σ-algebra , for each , contains the negligible sets so that an equality between two random variables is understood up to a negligible set.
2 is called a Castaing representation of .