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Regular version of the site
Master 2023/2024

Actuarial Сalculus

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Area of studies: Economics
When: 1 year, 1-3 module
Mode of studies: offline
Open to: students of one campus
Master’s programme: Stochastic Modelling in Economics and Finance
Language: English
ECTS credits: 9
Contact hours: 84

Course Syllabus

Abstract

The basic topics of this course are compatible with official material of actuarial education in UK and other parts of the world. The course contains important material on topics that are relevant for recent insurance and actuarial developments. The first part of the course is focused on basic actuarial mathematics and life insurance. The second part of the course concentrates on risk theory where one of the topics is to estimate the ruin probability of an insurance company when its surplus is modelled by a Cramér-Lundberg process.

Learning Objectives

• The aim of this course is to provide the skills for basic actuarial calculations both in life and non-life insurance as well as understanding the basic principles behind these calculations.
• This course is highly theoretical and the greater focus is on mathematics behind the algorithms, not on obtaining data from Internet and not on software implementation. However, an important objective is operational knowledge of the studied techniques, say the use of actuarial tables, hence there will be a practical side to the course as well.
• By the end of the course students will have a broad view of applications, including the most recent and state-of-the-art developments in actuarial science.

Expected Learning Outcomes

• • Understanding and ability to present/describe the methods studied in this course in mathematical terms. • Application of these methods to problems/examples. • Understanding the limitations and benefits related to using of different actuarial techniques. • Implementing methods studied in the course with Mathematica and/or statistical software. • Efficient work in groups.
• Understanding and ability to present/describe the methods studied in this course in mathematical terms.
• Application of these methods to problems/examples.
• Understanding the limitations and benefits related to using of different actuarial techniques
• Implementing methods studied in the course with Mathematica and/or statistical software.
• Efficient work in groups.

Course Contents

• Тема 1. Basic Actuarial Mathematics
• Тема 2. Life Insurance
• Тема 3. Premiums, reserves and risks
• Тема 4. Multiple Life Insurance
• Тема 5. Risk models
• Тема 6. Utility Theory
• Tema 7. Credibility Theory
• Tema 8. Claims Reserving
• Tema 9. The Cramér–Lundberg Model

Assessment Elements

• Intermediate Exam
At the end of Module 2, the student must present an intermediate exam.
• Exam
At the end of module 3, the student must present an exam
• Quizzes
In each module, the student must present three quizzes.

Interim Assessment

• 2023/2024 2nd module
0.55 * Intermediate Exam + 0.225 * Quizzes + 0.225 * Quizzes
• 2023/2024 3rd module
0.55 * Exam + 0.45 * Quizzes

Recommended Core Bibliography

• Actuarial Mathematics, Bowers, N. L., 1986
• Actuarial models : the mathematics of insurance, Rotar, V. I., 2007
• Alternative risk transfer : integrated risk management through insurance, reinsurance, and the capital markets, Banks, E., 2005
• An introduction to actuarial mathematics, Gupta, A. K., 2002
• Applied insurance analytics: a framework for driving more value from data assets, technologies, a..., Saporito, P.L., 2014
• Applied stochastic models and control for finance and insurance, Tapiero, C. S., 1998
• Changes in the life insurance industry: efficiency, technology and risk management, , 2002
• German utility theory : analysis and translations, Chipman, J. S., 2014
• Life insurance : the centennial edition, 1915-2015, Black, K., 2015
• Life insurance mathematics, Gerber, H. U., 1995
• Non-life insurance mathematics : an introduction with stochastic processes, Mikosch, T., 2004
• Non-life insurance mathematics, Straub, E., 1997
• Stochastic models in life insurance, Koller, M., 2012
• Боровков А. А. - Математическая статистика - Издательство "Лань" - 2010 - 704с. - ISBN: 978-5-8114-1013-2 - Текст электронный // ЭБС ЛАНЬ - URL: https://e.lanbook.com/book/3810