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Quantitative Risk Management Using Copulas

FMSN65 / MASM33,    7,5 credits, A (Second Cycle)

General Information

Elective for: F5, F5-fm, I5-fir, Pi5,R5, Master Mathematical Statistics
Language of instruction: The course will be given in English

Contents

Multivariate distributions including, normal, students-t, spherical, elliptical and parametric mixture distributions. Measures of association such as: Pearson’s correlation,  Kendall’s tau, and Spearman’s rho.Properties of copulas; spherical, elliptical, and Archimedean copulas; simulation of copulas.Some theoretical background for univariate extreme value theory and max-stable distributions in the bivariate case. Methods for constructing multivariate models in higher dimensions: copula representations, Sklar’s theorem and the Fréchet-Hoeffding bounds for joint distributions.Statistical inference for copulas and multivariate extreme-value distributions; including multivariate peak over threshold, maximum likelihood, as well as CFG and Pickand’s non-parametric estimators.

Examination details

LTH:

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam and computer labs with written reports.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0121. Name: Written Examination.
Credits: 6. Grading scale: TH. Assessment: Written examination.
Code: 0221. Name: Laboratory Work.

NF:

2101 Examination, 6,0 hp
Grading scale: Fail, Pass, Pass with distinction
2102 Computer exercises, 1,5 hp
Grading scale: Fail, Pass
Computer exercises with written reports.

Admission

Admission requirements LTH:

Assumed prior knowledge: FMSN55 Links to an external site. Statistical Modelling of Extreme Values

 

Entry requirements Science faculty:

For admission to the course English 6/B and knowledge equivalent to 90 ECTS credits
within the subjects of mathematics or mathematical statistics is required. 7,5
ECTS credits must be on an advanced level, the remaining 82.5 ECTS credits may be
on a basic or advanced level. Among these 90 ECTS credits knowledge equivalent to
MASM15, Mathematical Statistics: Statistical Modelling of Extreme Values, 7.5 credits
is required

Reading list

  • Jan Beirlant, Yuri Goegebeur, Johan Segers, Jozef Teugels: Statistics of Extremes: Theory and Applications. Wiley, 2004, ISBN: 978-0471976479.
  • Jan-Frederik Mai and Matthias Scherer: Simulation copulas, stochastic models, sampling algorithms, and applications. Imperial College Press, 2017, ISBN: 978-1848168749.

Contact and other information

Director of studies: studierektor@matstat.lu.se
The number of participants is not limited.

The course overlaps following course/s: FMSN15 Links to an external site., MASM23, MASM33

Official Course Description