Actuarial Calculus -2

Master 2024/2025

Type: Elective course (Stochastic Modeling in Economics and Finance)

Delivered by: Department of Statistics and Data Analysis

When: 1 year, 3 module

Open to: students of all HSE University campuses

Language: English

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.