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Yoshihiro Ryu

Publications and source records attributed to Yoshihiro Ryu.

5 recordsLinked to original sources
arXiv2020

Generalized Filtrations and Its Application to Binomial Asset Pricing Models

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.

q-fin.MF↗
arXiv2019

A Binomial Asset Pricing Model in a Categorical Setting

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.

q-fin.MF↗
arXiv2018

A Category of Probability Spaces

We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving direction of information with a way of its interpretation. We introduce a contravariant functor E from Prob to Set, the category of sets. The functor E provides conditional expectations along arrows in Prob, which are generalizations of the classical conditional expectations. For a Prob arrow f, we introduce two concepts f-measurability and f-independence and investigate their interaction with conditional expectations along f. We also show that the completion of probability spaces is naturally formulated as an endofunctor of Prob.

math.PR↗
arXiv2017

Monetary value measures in a category of probability spaces

We generalize the notion of monetary value measures developed with category theory in [Adachi, 2014] by extending their base category from the category \c{hi} to the category of probability spaces Prob introduced in [Adachi and Ryu, 2016].

q-fin.MF↗