# NMAK17007U Monte Carlo Methods in Insurance and Finance

Volume 2024/2025
Education

MSc programme in Actuarial Mathematics

MSc Programme in Mathematics-Economics

MSc Programme in Statistics

Content

This will be an introductory course on Monte Carlo simulation techniques. Topics will include: basic principles and sampling methods; variance reduction; quasi-Monte Carlo; discretization methods for stochastic differential equations; applications. Monte Carlo methods are of applied relevance because real-life problems in insurance, finance, and other applied areas are often too complicated to be solved using explicit analytical methods. When simulation is done naively, various problems can arise (e.g., the variance of the estimate may be large compared with the estimate). There are also methodological issues (e.g., effective means for generating random samples). Throughout the course, examples will be drawn from both insurance mathematics and finance.

Learning Outcome

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
• 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.

Sand2 and Mathematical Finance.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures per week for 7 weeks.
• Category
• Hours
• Lectures
• 28
• Preparation
• 177
• Exam
• 1
• Total
• 206
Written
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation time)
Exam registration requirements

The two mandatory assignments must both be passed in order to attend the oral exam.

Aid
All aids allowed
Marking scale