Stochastic analysis with applications (ΣΕΕ15)

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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.