Generalized Filtrations and Its Application to Binomial Asset Pricing Models

2020/11/17 by Takanori Adachi, Adachi, Takanori, Katsushi Nakajima +3 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · #16B50 #60G20 #91B25 #91Gxx #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Risk and Portfolio Optimization #Stochastic processes and financial applications #msc:16B50 #msc:60G20 #msc:91B25 #msc:91Gxx #q-fin.MF

paper · pdf · doi:10.48550/arxiv.2011.08531

18 pages

arxiv created 2020/11/17 · openalex publication_date 2020/11/17 · arxiv updated 2020/11/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

We introduce generalized filtration with which we can represent situations such as some agents forget information at some specific time. The filtration is defined as a functor to a category Prob whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement [Adachi and Ryu, 2019]. As an application of a generalized filtration, we develop a binomial asset pricing model, and investigate the valuations of financial claims along this type of non-standard filtrations.

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