Actuarial Calculus -2

2024/2025

Academic Year

ENG

Instruction in English

Delivered at:

Department of Statistics and Data Analysis

Course type:

Elective course

When:

1 year, 3 module

Instructor

Moreno-Franco, Harold A.

Course Syllabus

Abstract

In this second part of Actuarial Calculus, I will give an introduction to Risk Theory offers a comprehensive exploration of the mathematical and statistical foundations of risk analysis in insurance. The course covers essential topics such as compound risk models, the computation of claim distributions, premium calculation principles, and risk measures. It delves into utility theory, examining the Expected Utility Hypothesis and its implications for optimal insurance strategies and risk sharing. Additionally, the curriculum introduces the Cramér–Lundberg model, focusing on ruin probabilities, differential equations, reinsurance, and the concept of Time to Ruin. Overall, this course equips students with theoretical concepts and quantitative methods necessary for effective risk management, enabling them to evaluate insurance products and make informed decisions in real-world contexts.

Learning Objectives

• Understand and Analyze Compound Models and Discrete Distributions: To explore the structure and computation methods of compound risk models (S) and to calculate the distribution of S in the discrete case, identifying key approximations and their practical implications for insurance premium calculations.
• Evaluate Premium Calculation Principles and Risk Measures: To examine various premium calculation principles and risk measures, assessing how these elements contribute to effective risk management in insurance and how they can be influenced by the characteristics of the underlying risk models.
• Investigate Expected Utility Theory and Optimal Insurance Solutions: To delve into the concepts of the expected utility hypothesis and zero utility premium, focusing on how they inform decision-making processes for optimal insurance coverage and the positioning of insurers in the market.
• Explore the Cramér–Lundberg Model and Its Applications: To define the Cramér–Lundberg process and understand its significance in estimating ruin probabilities. This includes analyzing the differential equations involved, evaluating the impact of reinsurance on risk exposure, and exploring the role of claim size distributions in determining the time to ruin.

Expected Learning Outcomes

• Learn about the different risk models
• Explore various topics in utility theory as they apply to insurance companies.
• Study some topics in Credibility Theory
• Learn the Classical Claims Reserving Methods The Dirichlet Model
• Acquire knowledge about the Cramér-Lundberg model.

Course Contents

• Risk models
• Utility Theory
• Theory of credibility
• Reserving of Claims
• The model of Cramér-Lundberg

Assessment Elements

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

Interim Assessment

• 2024/2025 3rd module
  0.55 * Exam + 0.45 * Quizzes

Bibliography

Recommended Core Bibliography

• Practical Risk Theory for Actuaries, Daykin, C. D., 1996

Recommended Additional Bibliography

• An introduction to mathematical risk theory, Gerber, H. U., 1979
• Mathematical methods in risk theory, Buhlmann, H., 1996
• Modern actuarial risk theory : using R, Kaas, R., 2009
• Modern actuarial risk theory, Kaas, R., 2001

Authors

• Moreno Franko Garold Andres
• Panov Vladimir Aleksandrovich