Carlos Pereira dos Santos

By the end of this course a student should be able to:
1.1 apply fundamental results of one variable calculus.
1.2 use basic techniques of linear algebra.
1.3 apply fundamental results of vector calculus.
1.4 apply some basic results of measure theory and integration.
The student is also expected to:
2.1 become acquainted with some basic techniques of MATLAB programming.
2.2 be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
2.3 implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Introduction to MATLAB.
II. Sequences and metric spaces.
a) Facts about the real numbers
b) Sequences of real numbers.
c) Metric spaces.
III. Equations in one variable.
(a) Review of single variable calculus
(b) Numerical solutions of equations in one variable:
IV. Systems of linear and non-linear equations
(a) Some basic notions of linear algebra
(b) Direct and iterative methods for solving linear systems.
(c) Review of vector calculus.
(d) Newton's method for systems of (non-linear) equations.
V. Measure theory, integration and probability
(a) Riemann's integral.
(b) Introduction to Measure theory and the Lebesgue integral.
(c) Applications to Probability theory:

The final grade will be based on homework assignments (50%) and a final exam (50%).
The evaluation of the homework assignments is subjected to oral discussions.
The final exam has a minimum grade of 7.5 out of 20.
Due to the nature of the evaluation in this course, there is no 2nd chance exam.

Felipa Dias de Mello Sampayo

By the end of the semester the student should have
developed and be able to apply the following
competences:
A. Knowledge and understanding
- Model the behavior of economic agents;
- Be able to follow the relevant theory regarding these subjects.
B. Application of Knowledge
- Implement theoretical results and modelling
techniques fto perform research;
- Choose the appropriate conceptual, mathematical and graphical approaches to provide solutions for specific problems;
C. Learning
- Development of individual study methods, namely
problem solving and understanding of models and modelling techniques.

1. Consumer theory
2. Producer Theory
3. Markets

Methods of during the semester Assessment: Final exam (100%)

Alberto Lopez Martin

By the end of this course a student should be able to:
OA1.1 Determine, analytically and numerically, the solution to nonlinear optimization problems.
OA1.2 Determine and analyze, analytically and numerically, the solution to some difference equations.
OA1.3 Determine and analyze, analytically and numerically, the solution to some ordinary differential equations.
OA1.4 Apply algorithms of dynamic programming.

The student is also expected to:
OA2.1 Become acquainted with the basics of programming in MATLAB.
OA2.2 Be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
OA2.3 Implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Optimization in R^n.
(a) Unconstrained optimization: Necessary and sufficient conditions. Steepest descent. Newton and quasi-Newton methods.
(b) Non-linear constrained optimization: The Karush-Kuhn-Tucker conditions. Penalty methods.

II. Difference equations.
(a) Linear difference equations.
(b) Some notable non-linear equations.
(c) Equilibrium points.
(d) Markov Chains.
(e) Applications: compound interests and gambler's ruin.

III. Ordinary differential equations.
(a) Some notable ODEs.
(b) Existence, uniqueness and qualitative methods.
(c) Euler's method and friends.
(d) Applications: dynamical interest rates, geometric Brownian motion, demographic models and turbulence.

IV. Dynamic programming.
(a) Dynamic programming in discrete time.
(b) Dynamic programming in continuous time.
(c) Optimal control.
(d) Numerical methods.
(e) Applications: modelling sustainable development and money in the utility.

The final grade will be based on 3 homework assignments in groups of 2 or 3 elements (60%) and a final exam (40%) with a minimum grade of 8/20.
Due to the nature of the evaluation in this course, there is no resitting exam.

Students may have to undertake an oral examination whenever the instructor seems it necessary.

João António Madeira

The main learning objectives of this course are to develop skills to analyse, summarize and to have a critical opinion about the following items: (i) Solow growth model; (ii) neoclassical view of macroeconomics, focused on the notions of general equilibrium, optimizing behaviour, and real cycles; (iii) Keynesian view of macroeconomics, focused on the notions of imperfect competition, price rigidity, and relevance of economic policy; (iv) simulation and estimation of business cycle models.

Dynamic Macroeconomics: Textbook Models
- Solow growth model
- Dynamic stochastic general equilibrium models
- Real business cycle models
- New-Keynesian macro models
- Simulation and estimation of DSGE models

There are two types of assessment.

The first type consists of assessment throughout the semester, in which the following instruments will be used: individual work (40%) and knowledge assessment exam (60%). This assessment type requires meeting a minimum attendance criterion of 60%. There is no minimum grade requirement for maintenance in assessment throughout the semester.

The second type consists of assessment by exam, in this case the assessment exam has a weight of 100%.

André Teixeira

1. Follow and understand current research topics in the field of Finance.

Attendance of the BRU-IUL and Finance department research seminar series, where papers will be presented in the following topics:
1. Asset Pricing
2. Corporate Finance
3. Derivatives
4. Risk Management

Students must be present at all research seminars. In each seminar students should debate the paper being presented with the presenter. Additionally, at the beginning of each seminar they should turn it a critical summary of the theme being debated. The final grade is the arithmetic average of the grade in these two components.
There is no 2nd chance evaluation.

José Dias Curto

At the end of the course, students must:
1) Know and use dynamic models with stationary and non-stationary variables.
2) Know and use multivariate models.
3) Be able to work with R and RStudio programs.

1) Dynamic models, stationarity and unit root.
2) VARMA models.
3) Univariate and multivariate GARCH models.
4) Cointegration, structural breaks and VECM models.

Assessment takes place through continuous assessment throughout the semester or assessment by exam. Continuous assessment throughout the semester consists of a group work (50%) and a test (50%) that covers the entire subject and whose grade must be greater than or equal to 7.5. Continuous assessment throughout the semester requires a minimum attendance of 66.67% of classes. Assessment by exam consists of carrying out an exam with a weighting of 100%. In the test and exam, students can use a calculator and all the materials provided by the teacher.

João Pedro Ruas

At the end of this course, each student should be able to:
1. Identify the main challenges of choice under uncertainty
2. Price financial assets using an equilibrium approach
3. Price financial assets using an arbitrage approach
4. Read a significant range of research papers in asset pricing and understand the main issues being discussed.

1. Choice theory
2. Portfolio theory
3. Equilibrium Pricing
4. Arbitrage Pricing

Students can choose between assessment throughout the semester or assessment by exam.

The assessment throughout the semester consists of:
- Individual works (50% of the final grade)
- One written test (50% of the final grade)

The assessment by exam consists of:
- One written test (100% of the final grade)

Passing the course depends on obtaining a final grade, rounded to the nearest interest, equal to or greater than 10.

Thomas Greve

At the end of the course, the student should be able to:
LG1. Analyse the main theoretical models of mechanism design and auction theory;
LG2. Apply the theoretical concepts to practical applications; and
LG3. Develop a critical assessment of research articles in the area of microeconomics with a focus on topics in mechanism design and auction theory.

P1. Auctions with single unit sale
P2. Mechanism Design
P3. Interdependent values
P4. Multi-unit (identical) auctions
P5. Multiple Object auctions
P6. Applications

The assessment elements and their respective weightings are as follows:
a) 40% presentation of a scientific article (preferably still in an unpublished working paper version) and a peer-review report on the chosen article.
b) 60% final exam (with a minimum mark of 8).

Joaquim Ramalho

By the end of the unit, the student should have achieved the following learning goals (LG):
OA1. Know and apply regression models to cross-sectional or panel data
OA2. Know how to choose and specify econometric models for unlimited or limited continuous dependent variables
OA3. Know how to choose and specify econometric models for discrete dependent variables
OA4. Know how to estimate, evaluate and interpret econometric models
OA5. Know how to evaluate and solve endogeneity problems
OA6. Be able to work with econometric packages

S1. Introduction
S2. Linear Regression Analysis
S3. Nonlinear Regression Analysis
S4. Discrete Choice Models
S5. Models for Limited Dependent Variables

The students are assessed throughout the semester, with the final grade being based on two components: i) two problem sets (weight: 25% each); ii) a written (open book) exam (weight: 50%). To get approval, students must fulfill the following criteria: i) weighted mean of at least 9,5/20; ii) minimum grade at the exam and each problem set of 7,5/20. Students may also be evaluated through a final (open book) exam accounting for 100% of the grade. There are no re-sitting exams.

Develop writing and research skills to conduct independent and original research in the field of Finance.

Development of the research project that will form the basis for the student`s dissertation work.

Students must submit a research project containing their proposal for the required three original research papers to be developed during their dissertation.
The report will be reviewed by two faculty members chosen by the Director of the Doctoral Program.
There is no 2nd chance evaluation.

Szabolcs Sebestyén

1. Understand the econometric methods used in empirical asset pricing
2. Be able to specify and implement empirical asset pricing models

1. Model specification and estimation strategies
2. Affine processes
3. Pricing kernels and factor models

To accomplish the learning goals, the following learning-teaching methodologies (LTM) will be used:
1. Expositional, to the presentation of the theoretical reference frames
2. Showing computer codes for the different models used (Rstudio and Matlab)
3. Active, with the realization of individual works
4. Self-study, related with autonomous work by the student, as is contemplated in the Class Planning.

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The evaluation has two parts. First, the students must carry out an empirical project where they specify and implement an asset pricing model with empirical data. Second, they present an empirical asset pricing paper.

Mohamed Azzim

At the end of this learning unit, students should develop a clear and systematic understanding of the main corporate finance theories and their applications:
1. Corporate governance;
2. Asymmetric information, incentives and (financial and economic) distress;
3. Investments, diversification and acquisitions;
4. Capital structure and financing;
5. Payout to shareholders.

1. Introduction to the main corporate finance theories and their applications.
2. Corporate governance.
3. Asymmetric information, incentives and (financial and economic) distress.
4. Investment, diversification and acquisition.
5. Capital structure and financing.
6. Payout to shareholders.
7. Reflection on main corporate finance theories and their applications.

The final grade will be based on three components:
1. Written and oral communication of referee reports on papers related to each of the topics of the syllabus (40%);
2. Written and oral presentation of a literature review (30%);
3. Written and oral presentation of a research project (30%).
Notes:
a. The final grade will be provided after an individual self-assessment report meeting with each student.
b. There is no exam as assessment is based on individual research of the student.

João Pedro Ruas

1. Follow and understand current research topics in the field of Finance.

Attendance of the BRU-IUL and Finance department research seminar series, where papers will be presented in the following topics:
1. Asset Pricing
2. Corporate Finance
3. Derivatives
4. Risk Management

Students must be present at all research seminars. In each seminar students should debate the paper being presented with the presenter. Additionally, at the beginning of each seminar they should turn it a critical summary of the theme being debated. The final grade is the arithmetic average of the grade in these two components.
There is no 2nd chance evaluation.

José Carlos Dias

At the end of the course, a successful student should be able to:
1. Knowing how to build an arbitrage strategy with options.
2. Use the main tools of stochastic calculus.
3. Being able to use and derive the Black-Scholes-Merton model.
4. Knowing how to build a dynamic hedging strategy.
5. Being able to implement models with local volatility, stochastic volatility and jumps.
6. Being able to price numerically and analytically American-style options.
7. Being able to price numerically and analytically real options.
8. Being able to price numerically and analytically volatility derivatives.

1. Discrete time theory and martingale pricing

2. Stochastic calculus for finance

3. Black-Scholes-Merton model, the Greeks and the implied volatility surface

4. Local volatility and stochastic volatility models

5. Markovian diffusion processes with killing and Lévy processes

6. American-style options and numerical methods for option pricing

7. Modeling and pricing real options

8. Modeling and pricing volatility derivatives

Students can choose between assessment throughout the semester or assessment by exam.

The assessment throughout the semester consists of:
- Individual replication work (50% of the final grade).
- One written test (50% of the final grade).

The assessment by exam consists of:
- One written test (100% of the final grade).

Passing the course depends on obtaining a final grade, rounded to the nearest interest, equal to or greater than 10.

Students who successfully complete this course should be able to:
1. To design, project, adapt and perform original research that meets the requirements of academic quality and integrity and contribute to expand the frontiers of knowledge in Finance;
2. To communicate the results of such research to peers and the academic community in general, including their dissemination through national or international publications with referees.

The nature of the Course does not allow to define a syllabus with concrete subjects.
More important than the transmission of new knowledge, this course aims to apply the skills already acquired to achieve the ultimate goal of completing the thesis. Thus, the syllabus will be set each year based on research projects presented and implemented by the doctoral students, trying to find, through the presentation and discussion of completed or in progress research, the foundations for a better theoretical and empirical contextualization of the student’s work.

At the end of the second and third years a committee will assess the PhD Student/Candidate’s Written Report and its oral presentation, which represents his/her research progress.

The panel members have to write a short justification for the mark they decide to ascribe.

The defense of the thesis is presented when the student and the thesis committee agree that the thesis is essentially completed.