en مدل های شبیه سازی و احتمالی Simulation & Stochastic Models پژوهشي Research <span style="font-size:11pt"><span style="line-height:12pt"><span style="font-family:Cambria,serif"><span lang="EN-US" style="font-size:10.0pt"><span cambria="" math="" style="font-family:">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.</span></span></span></span></span><br> &nbsp; Life insurance,actuarial science,stochastic processes,Brownian motion. 1 8 http://ijiepr.iust.ac.ir/browse.php?a_code=A-10-2521-2&slc_lang=en&sid=1 Luis Ceferino Franco-Arbeláez luis.lfranco@gmail.com 180031947532846009191 180031947532846009191 Yes Instituto Tecnológico Metropolitano Luis Eduardo Franco-Ceballos luisefranco@itm.edu.co 180031947532846009192 180031947532846009192 No Instituto Tecnológico Metropolitano. Héctor Alonso Olivares-Aguayo hectoralonso.olivares@lasalle.mx 180031947532846009193 180031947532846009193 No Universidad La Salle México