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Магистратура 2019/2020

Актуарные расчеты

Направление: 38.04.01. Экономика
Когда читается: 1-й курс, 3, 4 модуль
Формат изучения: Full time
Прогр. обучения: Статистическое моделирование и актуарные расчеты
Язык: английский
Кредиты: 6

Программа дисциплины

Аннотация

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 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. The course refects the state-of-the-art in actuarial risk theory. 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 insurance and actuarial developments including the credibility theory, reserving, ranking of risks, modelling dependencies and the use of generalized linear models, as well as phase-type distributions with an eye on applications to the nonlife and actuarial developments including the credibility theory, reserving, ranking of risks, modelling dependencies and the use of generalized linear models, as well as phase-type distributions with an eye on applications to the nonlife insurance. The mathematical background assumed is on a level such as acquired in the bachelors programs in quantitative economics or mathematical statistics: Calculus, Probablity Theory, Mathematical Statistics, Linear Algebra and Insurance Mathematics.
Цель освоения дисциплины

Цель освоения дисциплины

  • 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.
Результаты освоения дисциплины

Результаты освоения дисциплины

  • 1. Understanding and ability to present/describe the methods studied in this course in mathematical terms 2. Application of these methods to problems/examples 3. Understanding the limitations and benefits related to using of different actuarial techniques 4. Implementing methods studied in the course with Mathematica and/or statistical software 5. Efficient work in groups
Содержание учебной дисциплины

Содержание учебной дисциплины

  • Premium principles and risk measures
  • Ordering risks
  • Background of Actuarial Mathematics
  • Population dynamics and epidemiology
  • Actuarial calculations: single life
  • Actuarial calculations: multiple lives
  • The Individual risk models
  • Collective risk models
  • Bonus-malus models
  • Insurance portfolio
  • Credibility Theory
  • Insurance and reinsurance
  • Phase-type distributions
  • Matrix-analytic methods
  • Elementary ruin theory
  • Ruin problems for L´evy processes
Элементы контроля

Элементы контроля

  • KP1 (неблокирующий)
  • examination (неблокирующий)
  • К/р2 (неблокирующий)
  • Д/З (неблокирующий)
Промежуточная аттестация

Промежуточная аттестация

  • Промежуточная аттестация (4 модуль)
    0.3 * examination + 0.2 * KP1 + 0.3 * Д/З + 0.2 * К/р2
Список литературы

Список литературы

Рекомендуемая основная литература

  • Actuarial Mathematics, Bowers N. L., Hickman J. C., 1986
  • Актуарные расчеты в негосударственном пенсионном и медицинском страховании, Четыркин Е. М., 2002
  • Актуарные расчеты. Ч.1: ., Миронкина, Ю. Н., 2018
  • Актуарные расчеты. Ч.1:, Миронкина, Ю. Н., 2017
  • Актуарные расчеты. Ч.2: ., Миронкина, Ю. Н., 2018
  • Актуарные расчеты. Ч.2:, Миронкина, Ю. Н., 2017

Рекомендуемая дополнительная литература

  • Актуарные расчеты в негосударственном пенсионном и медицинском страховании, 272 с., Четыркин, Е. М., 2002