43 citations · 49 across the 10 of their papers we have counts for
10 papers
A geometric model of synthetic filtrations via context-dependent time
Takanori Adachi
Classical filtrations in probability theory formalize the accumulation of information along a linear time axis: the past is unique and the present evolves into an uncertain future.…
Hierarchical Structure of Uncertainty
Takanori Adachi
We introduce a new concept called uncertainty spaces which is an extended concept of probability spaces. Then, we express n-layer uncertainty which we call hierarchical uncertainty…
Discrete signature and its application to finance
Takanori Adachi, Yusuke Naritomi
Signatures, one of the key concepts of rough path theory, have recently gained prominence as a means to find appropriate feature sets in machine learning systems. In this paper, in…
Generalized Filtrations and Its Application to Binomial Asset Pricing Models
Takanori Adachi, Katsushi Nakajima, Yoshihiro Ryu
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…
A Binomial Asset Pricing Model in a Categorical Setting
Takanori Adachi, Katsushi Nakajima, Yoshihiro Ryu
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 absolutel…
Market efficiency, liquidity, and multifractality of Bitcoin: A dynamic study
Tetsuya Takaishi, Takanori Adachi
This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst expo…
Monetary value measures in a category of probability spaces
Takanori Adachi, Yoshihiro Ryu
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 pr…
Multi-Dimensional Pass-Through and Welfare Measures under Imperfect Competition
Takanori Adachi, Michal Fabinger
This paper provides a comprehensive analysis of welfare measures when oligopolistic firms face multiple policy interventions and external changes under general forms of market dema…
A Category of Probability Spaces
Takanori Adachi, Yoshihiro Ryu
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…
A Framework for Analyzing Stochastic Jumps in Finance based on Belief and Knowledge
Takanori Adachi
We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to sto…