Financial optimization and asset management

Course objectives

Students learn how to formulate mathematical models to tackle relevant finance and asset management problems, in particular those related to Portfolio Selection. They are introduced to different quantitative analysis and decision tools, mainly based on Optimization and Mathematical Programming. In addition, they acquire the capacity of using, understanding, and developing computational tools suitable for the efficient solution of the models proposed. Particular goals 1) Knowledge and understanding. At the end of the course, students will have a sound knowledge of optimization theory and of the main algorithms to solve optimization problems. They will also know the main optimization models used in finance and particularly in Portfolio Selection and Asset Management. 2) Applying knowledge and understanding. This course will enable students to address several practical problems in finance and asset management with the aid of quantitative models and with the use of computational tools for their solution. For each specific problem they will know which is the best fitting model and they will be able to evaluate the output solutions also under a multicriteria viewpoint. 3) Making judgements. On the basis of the knowledge variety of models presented in the course and of the capacity of each of them to capture the essence of a problem, students will develop an attitude to critical thinking and rigorous reasoning, being aware of the relations between models and real problems to which they are applied. They will be able to structure a problem, identifying the fundamental elements that should be included in the model which represents it. 4) Communication skills. To deal with decision problems via the application of quantitative models it is necessary to know a proper formal language. Students will be asked to discuss models and present the arguments of the course, also in a group collaboration. They will be stimulated by the teacher to write models in their algebraic form and to illustrate them orally. This is important for the student to become familiar with the use of the formal language, but also to reach the capacity of illustrating and explaining the models to every possible interlocutor, possibly using a non-technical language, but however precise and rigorous. 5) Learning skills. During the course the students will be required to conduct autonomous researches, with possible support from the teacher when necessary, referring to the related literature and reading specific papers published in the scientific journals of the disciplinary field. Students will be subsequently capable to deepen and continue the studies in this field. More generally, they will acquire the capacity of performing bibliographic researches on a specific subject of their interest. This is also useful for the student for the future development of her/his master thesis.

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FEDERICA RICCA Lecturers' profile

Program - Frequency - Exams

Course program
1. Optimization models and techniques [24 hours]: Optimization and Mathematical Programming – Linear Programming (LP) – Geometrical interpretation of a Linear Program – The Simplex Method – Essentials of Duality in Linear Programming. Integer and Mixed Integer Linear Programs (ILP, MILP) – Essentials in solution algorithms for ILP and MILP – Essentials of multi-objective optimization. Essentials of Graphs and Networks and Network flow optimization models. 2. Applications in finance [16 hours]: Asset Liability models – Capital Budgeting – Portfolio Selection models: risk-return models, models based on stochastic dominance, risk diversification models, index tracking. 3. Computational Finance with Matlab [8 hours]: Introduction to Matlab – Financial data preparation and processing – Optimization tools in Matlab – Practical solution of financial models.
Prerequisites
Basic algebra – set theory essentials – equalities and inequalities – systems of linear equations – basics of Statistics.
Books
G. Cornuejols, J. Pena, R. Tutuncu (2018) – Optimization Methods in Finance, Cambridge Univ. Press, 2nd edition; P. Rardin, Optimization in Operations Research, Upper Saddle River, Prentice-Hall, 1998. F. Cesarone (2020), Computational Finance. MATLAB oriented modeling, Routledge-Giappichelli Studies in Business and Management Teacher's handouts.
Teaching mode
Traditional lessons
Frequency
Attendance is highly recommended for this course, both to ensure a full understanding of the theoretical topics covered in the syllabus and to support and strengthen the skills acquired in recognizing optimization models, applying them to economic and financial problems, implementing and solving them using specific optimization software, and critically discussing the solutions. Regular attendance is essential for completing the practical assignments and for being adequately prepared to develop the final project assigned at the end of the course.
Exam mode
There will be an extended oral exam on all the topics of the course. Students attending the classes develop a project requiring the implementation of some of the models described during the course. Their exam is based on the discussion of the outcome of the project and on a oral exam.
Bibliography
G.L. Thompson, S. Thore, Computational Economics, The Scientific Press;
Lesson mode
The course (worth 6 ECTS credits) is structured by alternating classroom lectures with practical sessions in a computer lab. For each theoretical/methodological topic presented during lectures, a corresponding lab session is dedicated to practical applications for solving financial optimization problems using a Solver (Excel/Matlab). In these sessions, students work on model formulation exercises, implement and solve them, and critically discuss the solutions in terms of their validity within the application context or the need to revise the model that generated them. In the first part of the course, lectures focus on illustrating the main optimization methods and models, along with the tools needed to learn how to formulate and analyze them. These are presented through small-scale educational examples, always within the context of economic and financial problems. Around the midpoint of the course, once students have acquired the basic tools, lectures shift to presenting more advanced optimization models that are relevant for studying a wide range of real-world financial problems. These applied cases form the basis for lab activities, where students are assigned group tasks developed collaboratively among peers, under the supervision of the instructor and with the possibility of consulting them when needed. In addition to in-class practical activities, students are also assigned independent tasks to be completed outside of class. For each assignment, students are given sufficient time to complete the work, and the solutions are then presented and discussed in a subsequent lesson. The practical activities aim to develop students’ independent analytical and problem-solving skills through the application of optimization models. To consolidate and assess the skills acquired, at the end of the course students are given the opportunity to develop a small final group project.
  • Lesson code10599982
  • Academic year2025/2026
  • CourseFinance and insurance
  • CurriculumFinancial risk and data analysis - in lingua inglese
  • Year2nd year
  • Semester1st semester
  • SSDSECS-S/06
  • CFU6