# 151-0520/01 – Insurance Mathematics (InsMt)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor RNDr. Jan Hrubeš Subject version guarantor RNDr. Jan Hrubeš Study level undergraduate or graduate Requirement Choice-compulsory Year 3 Semester winter Study language English Year of introduction 2004/2005 Year of cancellation 2010/2011 Intended for the faculties EKF Intended for study types Follow-up Master, Bachelor
Instruction secured by
HRU31 RNDr. Jan Hrubeš
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

The objectives of the lessons are to analyse the methods of the actuarial calculations in the context of their ancient development, to identify their conveniences and disadvantages, and to formulate the universal principals on which they are based. The students should understand them insomuch that they will be able to design new modifications of known calculations and to gauge their applicability in the practice.

Lectures
Tutorials
Project work

### Summary

The main goal of this subject is to acquaint the students with the most fundamental results of the present actuarial mathematics at the appropriate level - so that they will be able to work further on these topics creatively on their own. The students will be familiarized with the insurance risk models, the main demographic characteristics used in the life insurance, the models of the net premium and the gross premium calculation as well in the life- as in non-life insurance, the general principles of the premium reserves calculation and the reinsurance. The actual points related to the pension systems and the insurer?s solvency will be also discussed. The matter of the subject can be studied using the knowledge of the financial mathematics, the statistics, the spreadsheets (esp. MS Excel) and the very elementary knowledge of the algorithm development and the programming.

### Compulsory literature:

Promislow, Vavid S.: Fundamentals of Actuarial Mathematics. Chichester: Wiley, 2006. ISBN 0-07-070584-4. WILLIAMS, Chester A., SMITH, Michael L., YOUNG, Peter C.: Risk Management and insurance. 7nd ed. New York: MacGraw-Hill, 1995. ISBN 0-07-070584-4.

### Way of continuous check of knowledge in the course of semester

Project No 1 - Pure Endowment and Annuity Assurance with Simple Premium Project No 2 - Life Insurance with Simple Premium Project No 3 - Life Assurance with Current Premium

### E-learning

http://moodle.vsb.cz/vyuka/ kurs 151-320 Pojistná matematika

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Risk Models in Assurance Methods of Assurance Risk Evaluation Probability Distribution of Assurance Claims Principles of Insurance Premium Calculation Equivalence Principle Life Assurance - Mortality Modeling Decrementing Population Experience Tables Experience Tables Smoothing Time Shifting, Selection and Antiselection Risk Collective Risk Commutation Functions Basic Kinds of Life Assurance and their Evaluation General Rules of Life Assurance Life Assurance Premium Calculation Capital Assurance Annuity Assurance Gross Premium Health Aspects of Life Assurance Medical Underwriting Accident and Disability Insurance Private Health Insurance Multiple-Lives and Collective Assurance Life Insurance Reserves Net Reserve, Gross Reserve Saving and Risk Parts of the Insurance Premium Calculations based upon te Life Assurance Reserve Smart-Money Reduction in the Case of Default on Premium Payment Share in Profit Modern Life Assurance Approach and Products Profit Testing, Implicite Value of Life Insurance Company Investment Life Assurance Superannuation Scheme Contributory and Benefit Pension Schemes Superannuation Scheme Financing Tariff Groups and Basic Indicators in Non-Life Insurance Statistical Background and Indicators Non-Life Insurance Premium Calculations Non-Life Insurance Reserves Triangular schemes, Chain-Ladder Method Extraordinary Risk Composition Reserve Non-Life Insurance Mathematical Models Models of Insurance Claims, Insurance Loss, Compound Insurance Models Time Aspects of Insurance Models Bankrupcy Probability Bonus-Malus Systems Reinsurance Proportional Reinsurance Non-Proportional Reinsurance

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 45 (45) 0
Other task type Other task type 45  0
Examination Examination 55 (55) 0
Written examination Written examination 55  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (B6202) Economic Policy and Administration (6202R010) Finance (01) Finance P Czech Ostrava 3 Choice-compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R010) Finance (01) Finance P Czech Ostrava 3 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner