2017/05/05 by Christa Cuchiero, Cuchiero, Christa, Irene Klein +3
Economics, Econometrics and Finance · #60G48 #91B70 #91G99 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1705.02087
openalex publication_date 2017/05/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We present a version of the fundamental theorem of asset pricing (FTAP) for\ncontinuous time large financial markets with two filtrations in an\nLp-setting for 1 \≤ p < \∞. This extends the results of Yuri\nKabanov and Christophe Stricker citeKS:06 to continuous time and to a large\nfinancial market setting, however, still preserving the simplicity of the\ndiscrete time setting. On the other hand it generalizes Stricker's\nLp-version of FTAP citeS:90 towards a setting with two filtrations. We do\nneither assume that price processes are semi-martigales, (and it does not\nfollow due to trading with respect to the \smaller filtration) nor that\nprice processes have any path properties, neither any other particular property\nof the two filtrations in question, nor admissibility of portfolio wealth\nprocesses, but we rather go for a completely general (and realistic) result,\nwhere trading strategies are just predictable with respect to a smaller\nfiltration than the one generated by the price processes. Applications range\nfrom modeling trading with delayed information, trading on different time\ngrids, dealing with inaccurate price information, and randomization approaches\nto uncertainty.\n