Actuarial Mathematics

Major: Finance, Banking and Insurance
Code of subject: 6.072.00.O.030
Credits: 5.00
Department: Applied Mathematics
Lecturer: PhD, as. prof. Applied Mathematics Department, Gaiduchok O.V.
Semester: 5 семестр
Mode of study: денна
Мета вивчення дисципліни: To develop students' systematized theoretical knowledge of the basics of creating, researching, and practicing actuarial models, as well as the methodology of insurance calculations.
Завдання: The study of the discipline involves the formation and development of students' competencies: general: GC01. Ability to abstract thinking, analysis and synthesis. GC08. Ability to search, process and analyze information from various sources. professional: SC04. Ability to apply economic and mathematical methods and models to solve financial problems. SC10. Ability to identify, justify and take responsibility for professional decisions.
Learning outcomes: PO05. Possess methodological tools for diagnosing the state of financial systems (public finance, including budget and tax systems, finance of business entities, household finance, financial markets, banking system and insurance). PLO06. Apply appropriate economic and mathematical methods and models to solve financial problems. PLO 08. Apply specialized information systems, modern financial technologies and software products. PLO10. Identify sources and understand the methodology of determining and methods of obtaining economic data, collect and analyze the necessary financial information, calculate indicators that characterize the state of financial systems. PLO 13. To master general scientific and special methods of researching financial processes.
Required prior and related subjects: Previous academic disciplines 1. Statistics 2. Insurance 3. Economic and mathematical methods and models Related and subsequent disciplines 1. Insurance services
Summary of the subject: The course "Actuarial Mathematics" covers the methods of estimating cash flows in time, the basics of the construction and practical use of actuarial models, methods of conducting insurance calculations.
Опис: Introduction. Subject, purpose of actuarial mathematics, historical background of its development. Basic categories, principles, concepts of actuarial mathematics. The essence and features of actuarial calculations. Necessary sections on probability theory. Random event, its probability. Basic theorems of probability theory. Bernoulli's formula and its consequences. Limit theorems. The law of large numbers. Random variable. Distributions of discrete and continuous random variables. Numerical characteristics of distributions. Elements of financial mathematics in actuarial calculations. Operations of accretion and discounting in short- and long-term transactions. The essence of the principle of financial equivalence. Equivalence of interest rates. Measuring the effectiveness of financial transactions. Equivalence of payments. Conversion and consolidation of one-time payments. Elements of the theory of financial and insurance annuities. Mathematical characteristics and parameters of annuities. Classification of annuities. Equivalence and conversion of annuities. Application of annuities in insurance. Mortality tables, their numerical and probabilistic indicators. Use of mortality tables in insurance calculations. Life insurance. Construction of life insurance tariffs. Annuities in life insurance. Switching functions and their use. Pension insurance. Types of pension schemes. Determination of insurance net premiums in funded and insurance pension schemes. Probabilistic description of life expectancy. Some analytical laws of mortality.
Assessment methods and criteria: - Intermediate control (performing a calculated test); - Performing individual homework; - Defense of the abstract; - Final control (exam).
Критерії оцінювання результатів навчання: 1. Testing by topics in the VNS 2. Implementation and defense of an individual research task 3. Performing control works
Recommended books: Electronic educational and methodical complex for the course "Actuarial Mathematics" (authors: Gaiduchok O.V., Yaroshko S.M. 1. Financial mathematics: a textbook / Kutsyk P.O. [et al. 2. Kinash O.M., Sorokivskyi V.M., Papka (Sorokivska) M.V. Fundamentals of actuarial calculations. Study guide - Lviv: Ivan Franko National University of Lviv, 2012. 188 p. 3. Negrei M.V. Actuarial mathematics: a study guide / M.V. Negrei. - Lviv: Ivan Franko National University of Lviv, 2013. - 208 p. 4. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Marco Corazza, Claudio Pizzi, Springer-Verlag Italia 2010. 331p. 5. Khaletska Z.P. Fundamentals of actuarial mathematics: textbook / Z.P. Khaletska, Y.O. Dovgenko. Kropyvnytskyi: V.V. Vynnychenko CDPU, 2018. - 180 p. 6. Kopych I.M., Sorokivsky V.M., Cherkasova S.V., Sorokivska M.V. Actuarial calculations: textbook / I.M. Kopych, V.M. Sorokivsky, S.V. Cherkasova - Lviv: Novyi Svit - 2000, 2020. 214 p.