# 105.046 Advanced life insurance mathematics This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2012S 2011S 2010S 2009S 2008S 2007S 2006S 2005S 2004S

2009S, VU, 4.0h, 6.0EC

## Properties

• Semester hours: 4.0
• Credits: 6.0
• Type: VU Lecture and Exercise

## Aim of course

Introduction to modern and practically relevant methods of life insurance mathematics with emphasis on the Markovian model, stochastic interest and unit-linked policies.

## Subject of course

Types of life insurance, general model for life insurance, Markov chains with countable state space, Chapman-Kolmogorov equations, Markovian jump processes, forward and backward differential equations, interest as stochastic variable, deterministic and stochastic cash flows, single premiums, premium reserves, Thiele's differential equation for premium reserves, differential equation for higher moments, distribution function of the premium reserves, examples and problems coming from practice (payments during the year, guaranteed annuities, premium refund, pure endowments with stochastic interest, disability insurance), Hattendorff's theorem, unit-linked policies is a discrete and continuous-time financial market model, Black-Scholes formula, life insurance with stochastic interest, stochastic interest rate models, technical analysis (profit testing, embedded value)

## Lecturers

• Kainhofer, Reinhold

## Course dates

DayTimeDateLocationDescription
Wed15:00 - 19:0011.03.2009 - 30.06.2009Sem.R. DA grün 06A KAINHOFER
Advanced life insurance mathematics - Single appointments
DayDateTimeLocationDescription
Wed11.03.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed18.03.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed25.03.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed01.04.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed08.04.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed15.04.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed22.04.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed29.04.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed06.05.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed13.05.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed20.05.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed27.05.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed03.06.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed10.06.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed17.06.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER
Wed24.06.200915:00 - 19:00Sem.R. DA grün 06A KAINHOFER

## Examination modalities

Exercises and oral examination

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
066 400 Mathematics Mandatory elective
066 401 Statistics Mandatory elective
066 402 Mathematics in Science and Technology Mandatory elective
066 403 Mathematics in Economics Mandatory elective
066 404 Mathematics in Computer Science Mandatory elective
066 405 Financial and Actuarial Mathematics Mandatory2. Semester
066 405 Financial and Actuarial Mathematics Mandatory2. Semester
066 415 Actuarial Mathematics Mandatory2. Semester
860 Technical Mathematics Mandatory elective
864 Mathematics for Natural Sciences Mandatory elective
866 Economic Mathematics Mandatory elective
867 Statistics Mandatory elective
869 Mathematics in Computer Science Mandatory elective
873 Finance and Actuarial Mathematics Mandatory elective

## Literature

Lecture notes for this course are available. Siehe Downloads im TUWIS Michael Koller: Stochastische Modelle in der Lebensversicherung, Springer-Verlag (2000) Exercise sheets for the course: See downloads in TUWIS

German