Some Results on Skorokhod Embedding and Robust Hedging with Local Time

Julien Claisse (), Gaoyue Guo () and Pierre Henry-Labordère ()
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Julien Claisse: École Polytechnique
Gaoyue Guo: University of Oxford
Pierre Henry-Labordère: Société Générale

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 2, No 9, 569-597

Abstract: Abstract In this paper, we provide some results on Skorokhod embedding with local time and its applications to the robust hedging problem in finance. First we investigate the robust hedging of options depending on the local time by using the recently introduced stochastic control approach, in order to identify the optimal hedging strategies, as well as the market models that realize the extremal no-arbitrage prices. As a by-product, the optimality of Vallois’ Skorokhod embeddings is recovered. In addition, under appropriate conditions, we derive a new solution to the two-marginal Skorokhod embedding as a generalization of the Vallois solution. It turns out from our analysis that one needs to relax the monotonicity assumption on the embedding functions in order to embed a larger class of marginal distributions. Finally, in a full-marginal setting where the stopping times given by Vallois are well ordered, we construct a remarkable Markov martingale which provides a new example of fake Brownian motion.

Keywords: Skorokhod embedding; Model-free pricing; Robust hedging; Local time; Fake Brownian motion; 60G40; 60G44; 91G20; 91G80 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1201-5

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