On arbitrages arising from honest times

TL;DR

This paper investigates whether additional information from honest times in continuous financial markets can lead to arbitrage profits, finding that arbitrage opportunities are limited to specific times related to honest times.

Contribution

It explicitly characterizes the occurrence of arbitrage opportunities in relation to honest times using the theory of progressive filtration enlargement.

Findings

No arbitrage before an honest time

Arbitrage at and after an honest time

Stronger arbitrages only at the moment of honest time

Abstract

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.