Actuarial Mathematics

Yosuke Ito 📧

April 7, 2024

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Actuarial Mathematics is a theory in applied mathematics.This is mainly used for determining the prices of insurance products and evaluating the liability of a company associating with insurance contracts.It is related to calculus, probability theory and financial theory, etc. In this entry, I formalize the very basic part of Actuarial Mathematics in Isabelle/HOL.It includes the theory of interest, survival model, and life table.The theory of interest deals with interest rates, present value factors, an annuity certain, etc.The survival model is a probabilistic model that represents the human mortality.The life table is based on the survival model and used for practical calculations. I have already formalized the basic part of Actuarial Mathematics in Coq ( in a purely axiomatic manner.In contrast, Isabelle formalization is based on the probability theory and the survival model is developed as generally as possible.Such rigorous and general formulation seems very rare; at least I cannot find any similar documentation on the web. This formalization in Isabelle is still at an early stage, and I cannot guarantee the backward compatibility in the future development. If you heavily depend on this entry, please let me know. (Updated April 7th, 2024.)


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April 7, 2024
Added some lemmas with fractional age assumptions in the theory Life_Table. Modified the existing theories; contact the author for incompatible changes.
July 8, 2023
Added the theories Survival_Model, Life_Table and Examples. Updated the theories Preliminaries and Interest.
January 23, 2022
Submitted the theories Preliminaries and Interest.


Session Actuarial_Mathematics