Riesz spaces in mathematical economics

2022/2023
Programme:
Financial Mathematics, Second cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M5
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

The Arrow-Debreu model for exchange economies with a finite number of commodities and consumers.Kakutani fixed-point theorem.
A Walras equilibrium in a neoclassical exchange economy.Welfare theorems.
Riesz spaces. Linear functionals and linear operators.Riesz spaces of commodities and prices.Model for exchange economy with infinitedimensional space of commodities and countably many consumers.

Readings

C. D. Aliprantis, D. J. Brown, O. Burkinshaw: Existence and optimality of competitive equilibria, Springer-Verlag, Berlin, 1990.
C. D. Aliprantis: Problems in equilibrium theory, Springer-Verlag, Berlin, 1996.
C. D. Aliprantis, O. Burkinshaw: Locally solid Riesz spaces with applications to economics, Mathematical Surveys and Monographs 105, American Mathematical Society, Providence, RI, 2003.

Objectives and competences

Students learn about the application of the theory of Riesz spaces in mathematical economics. They get acquainted with
some models of exchange economies.

Intended learning outcomes

Knowledge and understanding:
Knowledge and understanding of the basic concepts of the theory Riesz spaces. The ability of its use in mathematical economics.
Application:
Using the theory of Riesz spaces on models of exchange economies.
Reflection:
Understanding of the theory and the ability to apply it to concrete examples.
Transferable skills:
Identifying and solving problems.Formulation of nonmathematical problems in mathematical language.Ability to use domestic and foreign literature.

Learning and teaching methods

Lectures, exercises, homeworks, consultations, seminars

Assessment

Homeworks
Exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Roman Drnovšek:
DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55. [COBISS-SI-ID 9480281]
DRNOVŠEK, Roman. On positive unipotent operators on Banach lattices. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2007, vol. 135, no. 12, str. 3833-3836. [COBISS-SI-ID 14382937]
DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238. [COBISS-SI-ID 16214617]
Marko Kandić:
KANDIĆ, Marko. Sets of matrices with singleton spectra generated by positive matrices. Linear Algebra and its Applications. [Print ed.]. 2016, vol. 496, str. 463-474. ISSN 0024-3795. [COBISS-SI-ID 17602137]
DRNOVŠEK, Roman, KANDIĆ, Marko. Positive operators as commutators of positive operators. Studia Mathematica. 2019, tom 245, str. 185-200. ISSN 0039-3223. [COBISS-SI-ID 18407769]
KANDIĆ, Marko, VAVPETIČ, Aleš. The countable sup property for lattices of continuous functions. Journal of mathematical analysis and applications. [Print ed.]. Sep. 2018, vol. 465, iss. 1, str. 588-603. ISSN 0022-247X. [COBISS-SI-ID 18406489]