Actuarial Calculus

Master 2024/2025

Type: Elective course (Stochastic Modeling in Economics and Finance)

Delivered by: Department of Statistics and Data Analysis

When: 1 year, 1, 2 module

Open to: students of all HSE University campuses

Language: English

Abstract

This study delves into the essential principles of actuarial calculus, providing a comprehensive framework for understanding cash-flow modeling and the valuation of financial instruments in the context of life insurance. Key topics include the mathematical foundations of interest accumulation, the evaluation of annuities and fixed-interest securities, and the application of stochastic models to represent random cash-flows. The course emphasizes the critical assessment of premiums, reserves, and risks, enabling participants to apply mathematical techniques in real-world scenarios. Furthermore, it introduces complex life insurance constructs, such as joint-life and last-survivor models, facilitating a holistic approach to risk management and product evaluation in today's dynamic financial environment.

Learning Objectives

To Develop Proficiency in Cash-Flow Modeling: Equip students with the fundamental mathematical skills required to construct and analyze cash-flow models, including techniques for interest accumulation, cash-flow valuation, and the assessment of yield on various financial products.
To Apply Actuarial Calculus in Life Insurance Evaluation: Enable learners to model future lifetimes and evaluate life insurance products, with a focus on calculating life annuities and understanding their implications on policy pricing and financial sustainability.
To Enhance Understanding of Premiums, Reserves, and Risk Assessment: Provide a thorough analysis of different premium structures (net and office) and the methodologies for calculating reserves and random policy values, while also exploring the complexities of multiple life insurance scenarios through the use of copulas and joint distributions.

Expected Learning Outcomes

Understand and have the abilities to present/describe the methods studied in this course in mathematical terms.
Understand the limitations and benefits related to using of different actuarial techniques
Implement methods studied in the course with Mathematica and/or statistical software.
Applicate of methods studied in the course to problems/examples.
Understand and have the abilities to present/describe the methods studied in life insurance.
Understand and have the abilities to present/describe the methods studied in Premiums, reserves and risks.
Understand and have the abilities to present/describe the methods studied in Multiple Life Insurance.

Course Contents

Тема 1. Basic Actuarial Mathematics
Тема 2. Life Insurance
Тема 3. Premiums, reserves and risks
Тема 4. Multiple Life Insurance

Assessment Elements

Exam
At the end of Module 2, the student must present an exam.
Quizzes

Interim Assessment

2024/2025 2nd module
0.55 * Exam + 0.225 * Quizzes + 0.225 * Quizzes

Bibliography

Recommended Core Bibliography

Encyclopedia of actuarial science. Vol.1: A-D, , 2004
Encyclopedia of actuarial science. Vol.2: E-N, , 2004
Encyclopedia of actuarial science. Vol.3: O-Z. Index, , 2004
Ferrari, J. R. (1968). Investment Life Insurance Versus Term Insurance and Separate Investment: A Determination of Expected-Return Equivalents. Journal of Risk & Insurance, 35(2), 181–198. https://doi.org/10.2307/250829
Financial and actuarial statistics : an introduction, Borowiak, D. S., 2014
Luca Regis (Ed.). (2018). Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance. Web server without geographic relation, Web server without geographic relation (org): MDPI AG - Multidisciplinary Digital Publishing Institute. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.E6FBC941
Steinar Ekern, & Svein-Arne Persson. (1996). Exotic Unit-Linked Life Insurance Contracts. The Geneva Risk and Insurance Review, (1), 35. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.a.pal.genrir.v21y1996i1p35.63
Боровков, А. А. Математическая статистика : учебник для вузов / А. А. Боровков. — 5-е изд., стер. — Санкт-Петербург : Лань, 2021. — 704 с. — ISBN 978-5-8114-7677-0. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/164711 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
Кельберт, М. Я. Вероятность и статистика в примерах и задачах : учебное пособие / М. Я. Кельберт, Ю. И. Сухов. — Москва : МЦНМО, [б. г.]. — Том 2 : Марковские цепи как отправная точка теории случайных процессов — 2010. — 560 с. — ISBN 978-5-94057-557-3. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/9354 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
Кельберт, М. Я. Вероятность и статистика в примерах и задачах : учебное пособие / М. Я. Кельберт, Ю. М. Сухов. — Москва : МЦНМО, [б. г.]. — Том I : Основные понятия теории вероятностей и математической статистики — 2007. — 456 с. — ISBN 978-5-94057-253-4. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/9353 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
Кельберт, М. Я. Вероятность и статистика в примерах и задачах / М. Я. Кельберт, Ю. М. Сухов. — Москва : МЦНМО, [б. г.]. — Том 3 : Теория информации и кодирования — 2016. — 567 с. — ISBN 978-5-4439-2377-2. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/80125 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.

Recommended Additional Bibliography

Actuarial Mathematics, Bowers, N. L., 1986
An introduction to actuarial mathematics, Gupta, A. K., 2002
An introduction to actuarial studies, Atkinson, M. E., 2011

Authors

MORENO FRANKO GAROLDANDRES

Course Syllabus