Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-61-19-M-7

Non-Life Insurance Mathematics (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-61-19-M-7 Non-Life Insurance Mathematics 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-61-19-K-7
Non-Life Insurance Mathematics
P 84 h 186 h - - PL1 9.0 WiSe
  • About [MAT-61-19-K-7]: Title: "Non-Life Insurance Mathematics"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86316 ("Non-Life Insurance Mathematics")

Evaluation of grades

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


Contents

  • Convolution and transforms,
  • Claim size distributions,
  • Individual risk model,
  • Collective risk models:
    • Claim number process,
    • Poisson process,
    • Renewal processes,
    • Total claim size distribution,
  • Risk Process,
  • Ruin theory and ruin probabilities,
  • Premium calculation,
  • Experience rating:
    • Bayes estimation,
    • Linear Bayes estimation (Bühlmann and Bühlmann-Straub model),
  • Reserves,
  • Reinsurance and risk sharing.

Competencies / intended learning achievements

Upon successful completion of the module students have acquired a complete overview of the modelling of loss levels, time of damage and the reserve process under the generalized Cramer-Lundberg model. They understand the mathematical foundations of ruin theory and premium calculation (in particular, the experience rating and the terms of loss reserves and reinsurance) and are able to apply them.

By completing the exercises, students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the course. They understand the proofs presented in the lecture and are able to reproduce and explain them. They can in particular outline the conditions and assumptions that are necessary for the validity of the statements.

Literature

  • H. Bühlmann: Mathematical Methods in Risk Theory,
  • R. Kaas, M. Goovaerts, J. Dhaene, M. Denuit: Modern Actuarial Risk Theory,
  • T. Mikosch: Non-Life Insurance: An Introduction with the Poisson Process,
  • E. Straub: Non-Life Insurance Mathematics.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-61-19-M-7]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Actuarial and Financial Mathematics [P] Compulsory
Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)