# A Binomial Asset Pricing Model in a Categorical Setting

## TL;DR

This paper develops a binomial asset pricing model within a categorical probability framework, incorporating generalized filtrations to model information loss, and explores valuation of financial claims under these conditions.

## Contribution

It introduces a novel categorical approach to asset pricing with generalized filtrations, capturing information loss scenarios not addressed by traditional models.

## Key findings

- Model accommodates agents forgetting information at specific times.
- Valuations of financial claims are analyzed under non-standard filtrations.
- Framework extends classical asset pricing to more realistic information dynamics.

## Abstract

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