A notion of essential supremum is developed when the uncertainty is measured
by a family of non-dominated and non-compact probability measures. It provides
new perspectives on super-replication and allows the Absence of Instantaneous
Profit (AIP) to be characterized

Carassus, Laurence

English

arXiv

When uncertainty is modelled by a set of non-dominated and non-compact
probability measures, a notion of essential supremum for a family of
real-valued functions is developed in terms of upper semi-analytic functions.
We show how the properties postulated on the initial functions carry over to
their quasi-sure essential supremum. We propose various applications to
financial problems with frictions. We analyse super-replication and prove a
bi-dual characterization of the super-hedging cost. We also study a weak
no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which
prices are finite. This requires new results on the aggregation of quasi-sure
statements

Quasi-sure essential supremum and applications to finance

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