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Monte Carlo Methods in Insurance and Finance
Provider: Faculty of Science

Activity no.: 5578-22-07-31 
Enrollment deadline: 21/11/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time21.11.2022, at: 08:00 - 27.01.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJeffrey F. Collamore    E-mail address: collamore@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupB
Exam formOral examination, 30 min. Without time for preparation
Exam formNo external censorship. Several internal examiners.
Exam detailsThe two mandatory assignments must both be passed in order to attend the oral exam.
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Preparation117.00
Theory exercises50.00
Lectures28.00
Practical exercises10.00
Exam1.00
Sum206.00
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; 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.

Teaching and learning methods
4 hours of lectures per week for 7 weeks.

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