### Abstract

Actuarial Mathematics is a theory in applied mathematics, which 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 (https://github.com/Yosuke-Ito-345/Actuary) 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 July 8th, 2023.)

### License

BSD License

### History

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.

### Topics

- Mathematics/Games and economics

### Session Actuarial_Mathematics

- Preliminaries
- Interest
- Survival_Model
- Life_Table
- Examples

## Cite

×

Actuarial_Mathematics-AFP

    @article{Actuarial_Mathematics-AFP,
      author  = {Yosuke Ito},
      title   = {Actuarial Mathematics},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2022},
      note    = {\url{https://isa-afp.org/entries/Actuarial_Mathematics.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Jan 25, 2022 : Isabelle2021-1