Ame2223 Syllabus
Ame2223 Syllabus
Ame2223 Syllabus
14.9.2022
Goals
• Study of functional equations in economics, and, in particular, dynamic systems in the
continuum. We will study, at an intermediate level, differential equations (ordinary,
partial and stochastic), optimisation of functionals, optimal control of differential
equations (ordinary, partial and stochastic) and (possibly) dynamic game theory.
• Application to some economic theory models from growth theory, dynamic general
equilibrium, age-structured models, dynamics of distribution, finance, stochastic dy-
namics, and dynamic games.
• If we have time, we will also cover some special topics: models with singularities and
models with thresholds.
Approach
• We will follow a heuristic approach: emphasise the characterisation of the dynamic
properties generated by several dynamic systems rather than trying to prove existence
and uniqueness of solutions to the generic functional equations. This is not a course
on functional analysis.
• All material will be posted at the course’s website. After its initial posting the class
notes and the problem sets may be changed along the semester. Warning: please
check the date of the document before downloading it.
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Assumed background
• Ideally: mathematics and economic theory at the level of the Masters in Economics,
Monetary and Financial Economics, Quantitative Finance (ISEG)
Topics covered
The main topics which will be covered are the following:
Distributed material
• Lecture notes: will be posted close to the day of the lecture (see last year webpage
for previous versions of the notes)
• Problem sets: with applications of the material taught. Disclaimer: these are seen
as problems allowing for the application of the subjects which are lectured. There is
no certainty that they are well posed or interesting. Solutions will not be provided,
although I am ready to answer and discuss specific issues which can arise in the
process of solving them.
Assessment
The assessment will be made by a final written open book (no electronic device consultation)
exam (see : regulamento da avaliação dos doutoramentos do ISEG). The questions will be
taken from, or will be similar, to the ones included in the problem sets.
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Sessions
Tentative scheduling of sessions:
session date session syllabus
1 15/09/2022 18:00 - 20:00 Presentation. Introduction.
2 22/09/2022 18:00 - 20:00 ODE: linear
3 29/09/2022 18:00 - 20:00 ODE: linear
4 06/10/2022 18:00 - 20:00 ODE: non-linear
5 13/10/2022 18:00 - 20:00 ODE: extensions, applications
6 20/10/2022 18:00 - 20:00 Deterministic optimal control of ODE: CV, PMP, DP
7 27/10/2022 18:00 - 20:00 Deterministic optimal control of ODE: extensions and applicatio
8 03/11/2022 18:00 - 20:00 First-order PDE
9 09/11/2022 18:00 - 20:00 Optimal control of first-order PDE
10 16/11/2022 18:00 - 20:00 Parabolic PDE
11 23/11/2022 18:00 - 20:00 Optimal control of parabolic PDE
12 30/11/2022 18:00 - 20:00 SDE
13 07/12/2022 18:00 - 20:00 Optimal control of SDE
Bibliography
General textbooks covering the topics which will be lectured are:
• ODE: Guckenheimer and Holmes (1990), Hale and Koçak (1991), Perko (1996).
• OC-ODE: Kamien and Schwartz (1991), Grass et al. (2008), Weber (2011).
• OC-SDE: Pham (2009), Seierstad (2009), Fleming and Rishel (1975), Chang (2004).
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References
Acemoglu, D. (2009). Introduction to Modern Economic Growth. Princeton University
Press.
Dockner, E., Jorgensen, S., Long, N. V., and Sorger, G. (2000). Differential Games in
Economics and Management Science. Cambridge University Press.
Grass, D., Caulkins, J. P., Feichtinger, G., Tragler, G., and Behrens, D. A. (2008). Optimal
Control of Nonlinear Processes. With Applications in Drugs, Corruption, and Terror.
Springer.
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Perko, L. (1996). Differential Equations and Dynamical Systems, 2nd Ed. Springer-Verlag.
Weber, T. A. (2011). Optimal Control Theory with Applications in Economics. The MIT
Press.
Other references will be given along the way and would be cited in the class-notes.
Software
Although this is not a course in numerical methods, the use of computers helps a lot in
solving, plotting the solutions, studying the dynamic properties, and estimating the models.
Useful software for solving differential equations:
• public license: