2016/04/19 by Anna Aksamit, Shuoqing Deng, Aksamit, Anna +5
Economics, Econometrics and Finance · #49M29 #60G05 #60G40 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Monetary Policy and Economic Impact #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1604.05517
openalex publication_date 2016/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate pricing-hedging duality for American options in discrete time\nfinancial models where some assets are traded dynamically and others, e.g. a\nfamily of European options, only statically. In the first part of the paper we\nconsider an abstract setting, which includes the classical case with a fixed\nreference probability measure as well as the robust framework with a\nnon-dominated family of probability measures. Our first insight is that by\nconsidering a (universal) enlargement of the space, we can see American options\nas European options and recover the pricing-hedging duality, which may fail in\nthe original formulation. This may be seen as a weak formulation of the\noriginal problem. Our second insight is that lack of duality is caused by the\nlack of dynamic consistency and hence a different enlargement with dynamic\nconsistency is sufficient to recover duality: it is enough to consider\n(fictitious) extensions of the market in which all the assets are traded\ndynamically. In the second part of the paper we study two important examples of\nrobust framework: the setup of Bouchard and Nutz (2015) and the martingale\noptimal transport setup of Beiglb "ock et al. (2013), and show that our general\nresults apply in both cases and allow us to obtain pricing-hedging duality for\nAmerican options.\n