A Proposal Based on Stochastic Differential Equations for Income

Abstract

Previous work has highlighted the need to apply stochastic modeling to understand the dynamics of phenomena occurring in the insurance industry. In this paper, for life insurance and applying a stochastic approach under efficient markets, we use survival probabilities and stochastic differential equations to model the actuarial reserve, changes in the constituted actuarial reserve, and estimated income over time. We present an application, sensitivity analysis, and discussion of the results using United States life tables.

Keywords

• life insurance
• actuarial science
• stochastic processes
• brownian motion.