Graduate Courses Outlines - Department of Mathematics
General
| School
|
School of Science
|
| Academic Unit
|
Department of Mathematics
|
| Level of Studies
|
Graduate
|
| Course Code
|
ΣΣΕ15
|
| Semester
|
2
|
| Course Title
|
Stochastic analysis with applications
|
| Independent Teaching Activities
|
Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
|
| Course Type
|
Specialized general knowledge
|
| Prerequisite Courses
|
-
|
| Language of Instruction and Examinations
|
Greek
|
| Is the Course Offered to Erasmus Students
|
Yes (in English, reading Course)
|
| Course Website (URL)
|
See eCourse, the Learning Management System maintained by the University of Ioannina.
|
Learning Outcomes
| Learning outcomes
|
The course learning outcomes are: the presentation of the theoretical and practical fundamental concepts within Ito calculus, martingale methods, stochastic differential equations and diffusion processes. The application of this theory within linear filtering, optimal stopping and stochastic control, financial derivative.
Upon successful completion of the course the student will be able to:
- know the main results and basic applications of stochastic Ito calculus
- understand stochastic differential equations
- understand of martingales in continuous time
- use numerical methods for stochastic differential equations
- use methods of stochastic analysis for modeling in different application areas
|
| General Competences
|
- Working independently
- Decision-making
- Adapting to new situations
- Production of free, creative and inductive thinking
- Synthesis of data and information, with the use of the necessary technology
- Working in an interdisciplinary environment
|
Syllabus
Stochastic processes in continuous time, processes adapted to an information flow, processes predictable with respect to an information flow, Brownian motion. Ito stochastic calculus. Martingales and representation theorems. Stochastic differential equations: existence and uniqueness of the solution. Theory of diffusions: Markov processes, Dynkin formula, Girsanov theorem. Applications: linear filtering, optimal stopping and stochastic control theory, Financial Derivatives.
Teaching and Learning Methods - Evaluation
| Delivery
|
Face-to-face
|
| Use of Information and Communications Technology
|
Use of ICT in communication with students
|
| Teaching Methods
|
| Activity
|
Semester Workload
|
| Lectures
|
39
|
| Independent study
|
70
|
| Study and analysis of bibliography, Fieldwork
|
78.5
|
| Course total
|
187.5
|
|
| Student Performance Evaluation
|
- LANGUAGE OF EVALUATION: Greek
- METHODS OF EVALUATION: written work (20%), Final exam (80%)
|
Attached Bibliography
- Karatzas I. and S. Shreve. Brownian Motion and Stochastic Calculus. Springer. 1998
- Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
- Oksendal B.: Stochastic Differential Equations, 6th edition. Springer 2007.
- Revuz D. and M. Yor. Continuous martingales and Brownian motion. Springer. 2001
- Rogers L.C. and D. Williams.Diffusions, Markov Processes and Martingales. Vol.1 and 2, Cambridge University Press. 2002
- Steele J. M., Stochastic Calculus and Financial Applications, 2001.
- [Περιοδικό / Journal] Stochastic Analysis and Applications.