# Analysis on Cohort Effects in view of Differential Geometry and its Applications

## TL;DR

This paper introduces a differential geometry-based method to quantify and compare birth cohort effects in mortality data across countries, enhancing existing models like Lee-Carter and APC.

## Contribution

It develops a novel geometric approach for measuring cohort effects, providing a quantitative comparison method and extending previous models with new applications.

## Key findings

- Effective measurement of cohort effects demonstrated across four countries.
- Enhanced Lee-Carter model with geometric cohort effect analysis.
- Applicable to multiple mortality models for improved demographic analysis.

## Abstract

This paper analyzes birth cohort effects and develops an approach which is based on differential geometry to identify and measure cohort effects in mortality data sets. The measurement is quantitative and provides a potential method to compare cohort effects among different countries or groups. Data sets of four countries (e.g. U.k., U.S., Canada and Japan) are taken as examples to explain our approach and applications of the measurement to a modified Lee-Carter model are analyzed. In fact, this paper is an upgrade version of our paper arXiv:1504.00327. There is a new section which gives applications of our approach based on the Lee-Carter and APC models.