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Магистратура 2020/2021

Актуарные расчеты

Направление: 38.04.01. Экономика
Когда читается: 1-й курс, 3, 4 модуль
Формат изучения: без онлайн-курса
Охват аудитории: для своего кампуса
Прогр. обучения: Статистическое моделирование и актуарные расчеты
Язык: английский
Кредиты: 6

Course Syllabus

Abstract

Apart from the introduction into the standard actuarial theory, this course handles various methods of solving popular problems of life insurance that are relevant for actuarial practice, for instance, the Tiele equations in Markovian environment, CLT for order statistics in Demography, analysis of mortgate-link or index-linked insurance policies. In addition to basic topics which 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 1 insurance and actuarial developments including the credibility theory, reserving, ranking of risks in life-insurance, modelling dependencies and the use of generalized linear models, as well as phase-type distributions with an eye on applications to the life insurance. The second part of the course concentrates on the different aspects of non-life insurance, it handles various methods of solving popular problems of non-live insurance that are relevant for actuarial practice, for instance, the rating of automobile insurance policies, premium principles and evaluation of contingencies in advanced ruin models. All methods, considered in this course, require only few assumptions about the probabilistic properties of the model, from which the data is obtained.
Learning Objectives

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

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.
Course Contents

Course Contents

  • Тема 1. Basic Actuarial Mathematics
    Cash-flow modelling and compound interest • Valuing Cash-flow • Annuities and fixed-interest securities • The yield of a cash-flow
  • Тема 2. Life Insurance
    • Modelling future lifetimes • Evaluation of life insurance products • Life annuities
  • Тема 3. Multiple Life Insurance
    • The joint-life status • The last-survivor status • The general symmetric status • Asymmetric annuities • Asymmetric insurance
  • Тема 4. Premiums, reserves and risks
    • Different types of premiums • Net premiums • Office premiums • Prospective policy values • Reserves and random policy values • Value-at-risk and related risk measures
  • Тема 5. Theories of Value
    • Expected Utility Theory • Expected Utility Theorem • Subjective Expected Utility (SEU) • The shape of the utility function • Changes in risk • Risk and rewards • Insurance decisions
  • Тема 6. Some advanced actuarial models
    • The individual risk model • Collective risk models • Ruin theory • Bonus-malus system • Ordering of risks • Credibility theory • Generalized linear models
Assessment Elements

Assessment Elements

  • non-blocking Контрольная работа 1
  • non-blocking Контрольная работа 2
  • non-blocking Работа в течении семестра
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.275 * Контрольная работа 1 + 0.275 * Контрольная работа 2 + 0.45 * Работа в течении семестра
Bibliography

Bibliography

Recommended Core Bibliography

  • 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

Recommended Additional Bibliography

  • Кельберт М.Я., Сухов Ю.М. - Вероятность и статистика в примерах и задачах. Т.3: Теория информации и кодирования - Московский центр непрерывного математического образования - 2016 - 567с. - ISBN: 978-5-4439-2377-2 - Текст электронный // ЭБС ЛАНЬ - URL: https://e.lanbook.com/book/80125