2015/02/23 by Erhan Bayraktar, Zhou Zhou, Bayraktar, Erhan +1
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1502.06681
openalex publication_date 2015/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a financial market where stocks are available for dynamic\ntrading, and European and American options are available for static trading\n(semi-static trading strategies). We assume that the American options are\ninfinitely divisible, and can only be bought but not sold. In the first part of\nthe paper, we work within the framework without model ambiguity. We first get\nthe fundamental theorem of asset pricing (FTAP). Using the FTAP, we get the\ndualities for the hedging prices of European and American options. Based on the\nhedging dualities, we also get the duality for the utility maximization. In the\nsecond part of the paper, we consider the market which admits non-dominated\nmodel uncertainty. We first establish the hedging result, and then using the\nhedging duality we further get the FTAP. Due to the technical difficulty\nstemming from the non-dominancy of the probability measure set, we use a\ndiscretization technique and apply the minimax theorem.\n