Actuarial Statistics

The goal of the course is to provide basic knowledge on Stochastic Processes used in actuarial and financial models, which are then used in subjects such as Survival Models, Life Insurance Pricing in General Insurance and those devoted to analysis Investment dynamic. SPECIFIC RESPONSIBILITIES: 1. Theoretical and basic properties of Stochastic Processes 2. Main models of stochastic processes 3. Use of the models to represent and evaluate real situations. Transversal competences: 1. Capacity for analysis and synthesis. 2. Knowledge of mathematical computing software. 3. Troubleshooting. 4. Teamwork. 5. Critical thinking. 6. Oral and written communication.

The program content is divided into four themes: #1. Introduction: Definition, basic notions and general classifications of probability and stochastic processes. 1.1. Insurance application models. 1.2. Techniques for calculating the risk premium. # 2. Markov Chains. Conditional expectation and martingales. 2.1. Introducction 2.2 Markov Chains in discrete time 2.3. Basic knowledge on Markov chains in continuous time. 2.4. Conditional expectation. 2.5. Martingales in discrete time: application to random walks. # 3. Poisson processes and theory of renewal 3.1. Introduction 3.2. Insurance application models: Ruin theory. 3.3. Introduction to theory of renewal. # 4. Brownian motion. 4.1. Introduction. 4.2. Martingale related to Brownian motion. 4.3. Finance Application models: binomial model and Black-Scholes model applied to financial derivatives.

Theory (4 ECTS) Theoretical classes with support material available on the Web (a collection guides / slides and exercises, basic bibliographic material and supplementary material for further study those issues in which they are most interested). Will develop fundamental concepts and skills of the course that students must acquire, and solve exercises by the teacher, encouraging students' active participation in solving them (both individually and in teams). PRACTICE (2 credits): Problem-solving lessons. Computer labs. Presentations and debates.