Optimization Methods in Finance

Year
1
Academic year
2023-2024
Code
02010527
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Elective
Level
2nd Cycle Studies - Mestrado

Recommended Prerequisites

Basic courses in (Differential and Integral) Calculus, Linear Algebra and Probability and Statistics.

Teaching Methods

The classes are essentially of expository style and include examples and exercises to apply the material being taught.

 Extensive tutorial time is offered to the students to support the solution of the homework assignments and preparation for the various exams

Learning Outcomes

The main goal is teaching the most relevant optimization models in finance and the mathematical properties of the corresponding optimization problems. One aims also at showing how to formulate optimization models with real data and how to use numerical techniques to solve problems within the scope of this modeling.

The course aims at developing the following skills: knowledge of mathematical results; ability to formulate and solve problems; building and using mathematical models for real world situations. On the personal level it also allows to develop self-learning skills and independent thinking.

Work Placement(s)

No

Syllabus

(1) Basic concepts on the formulation of optimization problems: convexity; existence and unicity of solutions; conic formulation; multiobjective formulation; robust formulation; stochastic formulation.

(2) Linear models for asset pricing and detection of arbitrage in option prices. The discrete version of the fundamental theorem of asset pricing. Linear integer models for the construction of index funds.

(3) Portfolio selection models: mean-variance Markowitz model; efficient frontier; mean-absolute deviation model; Black-Litterman model; adjustment and use of covariance matrices; robust models; value at risk and conditional value at risk.

(4) Models of multiple periods (the case of asset liability management).

Head Lecturer(s)

José Luís Esteves dos Santos

Assessment Methods

Continuous assessment
During the semester there are two mid-term exams (50-75% of the final grade) and a set of homework assignments (50-25% of the final grade) given every two or three other weeks and handed in individually.: 100.0%

Final assessment
The exercises in the homework assignments are mathematical problems or short numerical tasks. The final exam option consists of a single exam (100% of the final grade).: 100.0%

Bibliography

L.N. Vicente, Introdução à Matemática Financeira, Departamento de Matemática da FCTUC, 2006/2007.

G. Cornuejols, R. Tütüncü, Optimization Methods in Finance, Cambridge University Press, 2006.