Monte Carlo Methods in Insurance and Finance

Knowledge:  By the end of the course, the student should develop an understanding of: the basic principles of stochastic simulation, including the generation of random variables and sample paths; the basic principles of importance sampling and other standard variance reduction techniques; discretization methods for simulating stochastic differential equations; and quasi-Monte Carlo methods.

Skills:   The student should develop analytical and computational skills for running complex simulation experiments, involving theoretical knowledge of such techniques as importance sampling, and methods for generating complex stochastic processes.

Competencies:  At the conclusion of the course, the student should be able to generate a variety of random processes, including sample paths of a Brownian motion and of certain stochastic differential equations.  The student should develop a thorough understanding of, and be able to apply, the stadard methods for variance reduction, including importance sampling, control variates, antithetic variables, and stratified sampling.  Finally, the student should develop an understanding of the basic principles behind quasi-Monte Carlo methods.