Robust pricing–hedging dualities in continuous time

Zhaoxu Hou and Jan Obłój ()
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Zhaoxu Hou: University of Oxford
Jan Obłój: University of Oxford

Finance and Stochastics, 2018, vol. 22, issue 3, No 1, 567 pages

Abstract: Abstract We pursue a robust approach to pricing and hedging in mathematical finance. We consider a continuous-time setting in which some underlying assets and options, with continuous price paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland (Ann. Stat. 31:1413–1438, 2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. superreplication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows us to quantify the impact of making assumptions or gaining information. We obtain a general pricing–hedging duality result: the infimum over superhedging prices of an exotic option with payoff G $G$ is equal to the supremum of expectations of G $G$ under calibrated martingale measures. Our results include in particular the martingale optimal transport duality of Dolinsky and Soner (Probab. Theory Relat. Fields 160:391–427, 2014) and extend it to multiple dimensions, multiple maturities and beliefs which are invariant under time-changes. In a general setting with arbitrary beliefs and for a uniformly continuous G $G$ , the asserted duality holds between limiting values of perturbed problems.

Keywords: Robust pricing and hedging; Pricing–hedging duality; Martingale optimal transport; Path space restrictions; Pathwise modelling; 91G20; 91B24; 60G44 (search for similar items in EconPapers)
JEL-codes: C61 G13 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (29)

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DOI: 10.1007/s00780-018-0363-9

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