Mathematical Economics 1
A.Y. 2021/2022
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
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Frontal lessons and live streaming. In case of of variations in the emergency situation we shall move to synchronous distance learning (Microsoft Teams)
Course syllabus
1) Subjective probability and fair valuation of bets
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
Suggested prerequisites
1) Mathematical Finance 1
2) Advanced Probability
3) Functional Analysis
1) Mathematical Finance 1
2) Advanced Probability
3) Functional Analysis
Teaching methods
Taught lectures
Online forum for discussions
Implementation in R of economical models (optional)
Online forum for discussions
Implementation in R of economical models (optional)
Teaching Resources
Main reference
I. Gilboa, Theory od Decision under Uncertainty, Cambridge University Press, 2009.
Other useful books
1) H. Follmer A. Schied, Stochastic Finance, 3rd Edition, De Gruyter.
2) L.J. Savage, The Foundations of Statistics, 2nd Edition, dover Publications
3) D. Duffie, Dynamic Asset Pricing Theory, 3rd Edition, Princeton Univeristy Press
4) C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, 3rd Edition, Springer.
Scientific Articles
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) P. Wakker and H. Zank, State dependent expected utility for Savage's state space, Mathematics of Operation Research, 1999.
2) F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity Aversion, Robustness, and the Variational Representation of Preferences, Econometrica, 2006.
I. Gilboa, Theory od Decision under Uncertainty, Cambridge University Press, 2009.
Other useful books
1) H. Follmer A. Schied, Stochastic Finance, 3rd Edition, De Gruyter.
2) L.J. Savage, The Foundations of Statistics, 2nd Edition, dover Publications
3) D. Duffie, Dynamic Asset Pricing Theory, 3rd Edition, Princeton Univeristy Press
4) C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, 3rd Edition, Springer.
Scientific Articles
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) P. Wakker and H. Zank, State dependent expected utility for Savage's state space, Mathematics of Operation Research, 1999.
2) 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
Professor(s)
Reception:
On appointment
Department of Mathematics, office number 1038