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2016/2017

Research Seminar "Probability Theory. Analytical and Economic Applications 1"

Type: Optional course (faculty)
When: 1, 2 module
Language: English
ECTS credits: 3

Course Syllabus

Abstract

In this course we discuss various topics of modern probability theory, stochastic processes, and statistics. Special emphasis is given to probabilistic problems with strong analytic aspects and problems with applications in economy. Pre-requisites : Theory of Probability, Functional Analysis, Partial Differential Equations Course Type: elective
Learning Objectives

Learning Objectives

  • Acquire a familiarity with random processes used in economic models, in models of financial mathematics, and to use them for making predictions. Study of stochastic analysis, and of analytic methods in the theory of random variables.
Expected Learning Outcomes

Expected Learning Outcomes

  • The students will be expected to have an understanding of theoretical principles necessary for the construction of models used in economics. They should be able to apply methods of modern stochastic analysis, and of analytical methods from the theory of probability to the study of economics models
Course Contents

Course Contents

  • Measures on infinite dimensional spaces. Equivalence and singularity, Gaussian measure. Kolmogorov Theorem. Weak convergence and Prokhorov’s Theorem. Isoperimetric inequality, Sobolev inequality. Sobolev space. Convexity
  • Wiener processes. Stochastic integral, and Ito’s formula. Stochastic differential equations. Ornstein-Uhlenbeck process
Assessment Elements

Assessment Elements

  • non-blocking Task
  • non-blocking Final exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.7 * Final exam + 0.3 * Task
Bibliography

Bibliography

Recommended Core Bibliography

  • Statistics for business and economics, Newbold P., Carlson W. L., 2007

Recommended Additional Bibliography

  • A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, & M. I. Yadrenko. (2018). Probability Theory: Collection of Problems. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1790324