Some results on Skorokhod embedding and robust hedging with local time
From MaRDI portal
Publication:1626510
DOI10.1007/S10957-017-1201-5zbMath1402.60046arXiv1511.07230OpenAlexW2765939861MaRDI QIDQ1626510
Gaoyue Guo, Pierre Henry-Labordère, Julien Claisse
Publication date: 27 November 2018
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1511.07230
Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44) Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20)
Cites Work
- Unnamed Item
- Unnamed Item
- The maximum maximum of a martingale with given \(n\) marginals
- Model-independent bounds for option prices -- a mass transport approach
- Pathwise construction of stochastic integrals
- Martingale optimal transport and robust hedging in continuous time
- Robust pricing and hedging of double no-touch options
- Tightness and duality of martingale transport on the Skorokhod space
- Making Markov martingales meet marginals: With explicit constructions
- Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping
- The Skorokhod embedding problem and its offspring
- Some inequalities with local times in zero of a Brownian motion
- Robust hedging of the lookback option
- Root's barrier: construction, optimality and applications to variance options
- Optimal transport and Skorokhod embedding
- An iterated Azéma-Yor type embedding for finitely many marginals
- A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
- Robust Hedging of Barrier Options
- Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints
- On the Monotonicity Principle of Optimal Skorokhod Embedding Problem
- From local volatility to local Lévy models
- ROBUST BOUNDS FOR FORWARD START OPTIONS
- The maximum maximum of a martingale constrained by an intermediate law
Related Items (6)
The geometry of multi-marginal Skorokhod embedding ⋮ On the Root Solution to the Skorokhod Embedding Problem Given Full Marginals ⋮ Embedding of Walsh Brownian motion ⋮ Peacock geodesics in Wasserstein space ⋮ Computational methods for martingale optimal transport problems ⋮ Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints
This page was built for publication: Some results on Skorokhod embedding and robust hedging with local time
