# Monte Carlo Methods in Insurance and Finance

### Course 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.

Education

MSc programme in Actuarial Mathematics

MSc Programme in Mathematics-Economics

MSc Programme in Statistics

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.

4 hours of lectures per week for 7 weeks.

Sand2 and Mathematical Finance.

Academic qualifications equivalent to a BSc degree is recommended.

Written
ECTS
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
Censorship form
No external censorship
Several internal examiners
Re-exam

Same as the ordinary exam.

If the assignments were not approved before the ordinary exam they must be resubmitted at the latest two weeks before the beginning of the re-exam week.

##### Criteria for exam assessment

In order to obtain the grade of 12, the student should convincingly and accurately demonstrate the knowledge, skills and competences described under Learning Outcome.

Single subject courses (day)

• Category
• Hours
• Lectures
• 28
• Preparation
• 177
• Exam
• 1
• English
• 206

### Kursusinformation

Language
English
Course number
NMAK17007U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 2
Schedulegroup
B
Capacity
60
The number of places might be reduced if you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Jeffrey F. Collamore   (9-677370706571737669447165786c326f7932686f)
Saved on the 14-02-2024

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