Mathematical Economics 1
A.Y. 2024/2025
Learning objectives
Aim of this course is to cover some of the most important topics of the Theory of Decisions in the economic and financial field, involving techniques related to Functional Analysis and Probability.
Expected learning outcomes
Axiomatization of the preferences of an agent and their functional representation. Applications of Decision Theory to solve some problems of economical/financial equilibrium.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1) Subjective probability
2) Preferences on lotteries in the Von Neumann-Morgenstern theory
3) State dependent preferences
4) Robust Preferences and Ambiguity
5) Utility maximization, arbitrage theory and robust optimization
6) Theory of market equilibrium
2) Preferences on lotteries in the Von Neumann-Morgenstern theory
3) State dependent preferences
4) Robust Preferences and Ambiguity
5) Utility maximization, arbitrage theory and robust optimization
6) Theory of market equilibrium
Prerequisites for admission
Strongly suggested
1) Mathematical Finance 1
2) Advanced Probability
Weakly suggested
3) Functional Analysis
1) Mathematical Finance 1
2) Advanced Probability
Weakly suggested
3) Functional Analysis
Teaching methods
Taught lectures
Teaching Resources
Main references
1) I. Gilboa, Theory od Decision under Uncertainty, Cambridge University Press, 2009.
2) H. Follmer A. Schied, Stochastic Finance, 3rd Edition, De Gruyter.
Other references
3) L.J. Savage, The Foundations of Statistics, 2nd Edition, dover Publications
4) D. Duffie, Dynamic Asset Pricing Theory, 3rd Edition, Princeton Univeristy Press
5) C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, 3rd Edition, Springer.
Scientific papers
1) B. de Finetti, Sul significato soggettivo della probabilità, Fundamenta Mathematicae, 1931.
2) G. Debreu, Topological methods in cardinal utility theory, 1960, Standford University Press.
3) F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity Aversion, Robustness, and the Variational Representation of Preferences, Econometrica, 2006.
1) I. Gilboa, Theory od Decision under Uncertainty, Cambridge University Press, 2009.
2) H. Follmer A. Schied, Stochastic Finance, 3rd Edition, De Gruyter.
Other references
3) L.J. Savage, The Foundations of Statistics, 2nd Edition, dover Publications
4) D. Duffie, Dynamic Asset Pricing Theory, 3rd Edition, Princeton Univeristy Press
5) C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, 3rd Edition, Springer.
Scientific papers
1) B. de Finetti, Sul significato soggettivo della probabilità, Fundamenta Mathematicae, 1931.
2) G. Debreu, Topological methods in cardinal utility theory, 1960, Standford University Press.
3) F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity Aversion, Robustness, and the Variational Representation of Preferences, Econometrica, 2006.
Assessment methods and Criteria
Oral exam aimed at verifying the knowledge of the theoretical elements developed during the course.
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 6
Lessons: 42 hours
Professor:
Maggis Marco
Shifts:
Turno
Professor:
Maggis MarcoProfessor(s)
Reception:
On appointment
Department of Mathematics, office number 1038