Abstract
It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks. Combining existing aggregation and convex dual representation theorems, we derive duality results for the minimal price on the set of upper semicontinuous discounted claims.
Highlights
In this paper, we are concerned with convex duality for the minimal superhedging problem with non-zero shortfall risk in continuous time
It is well known that the minimal superhedging price of a contingent claim is too high for practical use
In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks
Summary
We are concerned with convex duality for the minimal superhedging problem with non-zero shortfall risk in continuous time. In the model-free framework, that is, when no probabilistic assumption is made, superhedging duality results include those in (Acciaio et al 2016; Beiglbock et al 2013; Cheridito et al 2017; Burzoni et al 2017; Burzoni 2016) in discrete time and (Dolinsky and Soner 2014; Hou and Obłoj 2018; Bartl et al 2019; Bartl et al.2020) in continuous time It is well-known that the minimal superhedging price is too high for practical use, and even higher under model uncertainty. We show that a suitable sequential closedness of the acceptance set A carries over to the sublevel sets of the superhedging functional, guaranteeing enough regularity to derive a convex dual representation; see Theorem 1 for a precise statement This will require the use of aggregation results developed by Soner et al (2011b).
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