This course provides a rigorous and hands-on exploration of numerical techniques used to model complex systems in finance and insurance. Students will learn how to simulate and analyze stochastic processes that underlie asset prices, risk dynamics, and actuarial models.

Key topics include the generation of random variables, simulation of stochastic differential equations, and advanced Monte Carlo methods such as variance reduction, multilevel and importance sampling, least-squares Monte Carlo, and Markov chain Monte Carlo for Bayesian inference. Emphasis is placed on both the theoretical foundations and practical implementation of these methods in real-world financial and insurance contexts.