This talk consists of two parts. In the first part of the talk, we give an overview of the actuarial science career path and my own work experience as an educator and advisor for an actuarial science program. Following this, a mathematical point of view on actuarial science will be introduced. We consider a regime-switching model for an insurance market with two companies in the context of a non-zero-sum game. The corresponding system of integro-differential Hamilton-Jacobi-Isaacs equations is constructed and the numerical solution is approximated using the Markov chain approximation method. We conclude the talk with some directions for future work.