In the context of a general continuous financial market model, we study whether the additional information associated with an honest time τ 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 τ, whereas classical arbitrage opportunities can be realised exactly at τ as well as after τ. Moreover, arbitrages of the first kind can only be obtained by starting to trade as soon as τ occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than no free lunch with vanishing risk. © 2014 Springer-Verlag Berlin Heidelberg.
On arbitrages arising with honest times
Claudio Fontana
;
2014
Abstract
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time τ 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 τ, whereas classical arbitrage opportunities can be realised exactly at τ as well as after τ. Moreover, arbitrages of the first kind can only be obtained by starting to trade as soon as τ occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than no free lunch with vanishing risk. © 2014 Springer-Verlag Berlin Heidelberg.
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