Module Handbook

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Module MAT-61-30-M-7

Risk Measures with Applications to Finance and Insurance (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-61-30-M-7 Risk Measures with Applications to Finance and Insurance 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-61-30-K-7
Risk Measures with Applications to Finance and Insurance
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-61-30-K-7]: Title: "Risk Measures with Applications to Finance and Insurance"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86385 ("Risk Measures with Applications to Finance and Insurance")

Evaluation of grades

The grade of the module examination is also the module grade.


  • Preferences and expected utility,
  • Axiomatic introduction of risk measures,
  • Robust representation of convex and coherent risk measures,
  • Examples: Value at Risk, Average Value at Risk, Short case, worst case,
  • Extensions: Semi Dynamic, dynamic, distribution-free risk measures,
  • Estimation of risk measures,
  • Rating systems:
    • Score-based ratings,
    • Utility based ratings of financial products,
    • Risk-classes for insurance products,
  • Credit risk: Structural models and reduced form models,
  • Applications:
    • Risk-based insurance premiums,
    • Portfolio optimization under risk constraints,
    • Credit derivatives.

Competencies / intended learning achievements

Students know and understand the basics of the axiomatic theory of risk measures. They can classify different risk measures and assess the advantages and disadvantages of specific risk measures in various fields of finance and insurance mathematics. They understand the proofs and are able to reproduce and explain them. They can critically assess the different rating procedures and methods for the measurement of credit risk.


H. Föllmer, A. Schied: Stochastic Finance: An Introduction in Discrete Time,

L. Rüschendorf: Mathematical Risk Analysis.

References to Module / Module Number [MAT-61-30-M-7]

Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)