NMAK14014U Monte Carlo Methods in Insurance and Finance (AAM)
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
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.
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.
- Category
- Hours
- Exam
- 1
- Lectures
- 28
- Practical exercises
- 10
- Preparation
- 117
- Theory exercises
- 50
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minOral exam without preparation.
- Exam registration requirements
- The two mandatory assignments must both be passed in order to attend the oral exam.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK14014U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- B (Mon 8-12 + Tues 13-17 + Fri 8-12)
- Course capacity
- 60
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Jeffrey F. Collamore (9-6b7774746975777a6d4875697c7036737d366c73)