Checking date: 09/07/2020

Course: 2020/2021

Stochastic processes
Study: Master in Actuarial and Financial Sciences (224)

Coordinating teacher: ALBARRAN LOZANO, IRENE

Department assigned to the subject: Department of Statistics

Type: Compulsory
ECTS Credits: 6.0 ECTS


Students are expected to have completed
Actuarial Statistics
Competences and skills that will be acquired and learning results.
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.
Description of contents: programme
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.
Learning activities and methodology
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.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
  • KIJIMA, M. . Stochastic processes with applications to finance. Chapman & Hall.. 2003
  • ROLSKI, T., SCHMIDLI, H., SCHMIDT, V., TEUGELS, J.. Stochastic Processes for Insurance and Finance. Wiley. . 1999
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • DURRET, R.. Essential of Stochastic Processes. Springer. 1999
  • KAO, E.P.C.. An Introduction to Stochastic Processes. Duxbury Press. 1997
  • ROSS, S.M. . Stochastic Processes. . John Wiley.. 1996
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus and the academic weekly planning may change due academic events or other reasons.