2016/2017
Научно-исследовательский семинар "Теория вероятностей. Аналитические и экономические приложения 2"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
3, 4 модуль
Язык:
английский
Кредиты:
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
- 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
- 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
- Wiener processes. Stochastic integral, and Ito’s formula. Stochastic differential equations. Ornstein-Uhlenbeck process
- Hedging and Black-Scholes formula. Stochastic models and local volatility. Other related themes, such as optimal control, Malliavin calculus
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