Актуарные расчеты-1

2025/2026

Статус: Маго-лего

Кто читает: Департамент статистики и анализа данных

Где читается: Факультет экономических наук

Когда читается: 1, 2 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Морено Франко Гарольд Андрес

Язык: английский

Кредиты: 6

Контактные часы: 56

Full Syllabus Ask Question

Abstract

Actuarial Calculus I develops a formal mathematical framework for valuing cash-flows whose amounts or payment times may be deterministic or uncertain. The course begins with the time value of money and deterministic cash-flow models, progresses to random cash-flows and elementary stochastic interest-rate models, and then introduces survival models and life-contingent payments. These tools are applied to life insurance benefits, life annuities, premiums, reserves, multiple-decrement models, and elementary multiple-state models. The course emphasizes definitions, assumptions, derivations, and the mathematical scope of each result. Numerical calculations and simulation support the theory but do not replace it.

Learning Objectives

To develop a rigorous mathematical understanding of the actuarial models and valuation principles studied in the course.
To connect the mathematical theory of cash-flow valuation, survival models, life-contingent benefits, premiums, and reserves with actuarial applications.
To develop the ability to formulate actuarial problems precisely, stating the relevant assumptions, notation, and scope of the model.
To develop the ability to analyse the benefits, limitations, and sensitivity of actuarial techniques with respect to their underlying assumptions.
To use computational tools, where appropriate, to support numerical calculations, simulation, and sensitivity analysis, without replacing mathematical justification.
To develop clear mathematical communication and effective problem-solving skills, both individually and in collaborative work.

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. Financial Actuarial Mathematics and Cash-flow Valuation
Тема 2. Survival Models and Life Contingencies
Тема 3. Premiums, Reserves, and Policy Risk
Тема 4. Multiple-Decrement and Elementary Multiple-State Models

Assessment Elements

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

Interim Assessment

2025/2026 2nd module
0.225 * Quizzes + 0.55 * Exam

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 Garold Andres

Course Syllabus