2015/11/23 by Julien Claisse, Claisse, Julien, Gaoyue Guo +4
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1511.07230
openalex publication_date 2015/11/23 · arxiv created 2017/10/30 · arxiv updated 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.