Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-61-30-K-7

Risk Measures with Applications to Finance and Insurance (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Additional informations
Livecycle-State [NORM] Active


Each winter semester at least one of the following courses will be offered:[MAT-61-15-K-7], [MAT-61-20-K-7], [MAT-61-30-K-7] or [MAT-61-31-K-7].

The lecture offer for the specialization module planned for the following three semesters will be made available on the website of the master's programme "Actuarial and Financial Mathematics".


  • 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.


Further literature will be announced in the lecture.

Requirements for attendance (informal)


Requirements for attendance (formal)


References to Course [MAT-61-30-K-7]

Module Name Context
[MAT-61-12A-M-7] Specialization Actuarial and Financial Mathematics WP: Obligation to choose in Obligation to choose-Modulteil #B 2V, 4.5 LP
[MAT-61-30-M-7] Risk Measures with Applications to Finance and Insurance P: Obligatory 2V, 4.5 LP