Learning objectives
During the course, students will be taught the fundamental elements of probability wich are at the basis of portfolio theory. Several principles underpinning financial mathematics are also provided. Finally, students will be shown how it is possible to represent the preferences of a rational decision maker and build an optimal portfolio in a market where the returns of listed securities and interaction between them are known. The methodologies will be implemented exclusively in the Matlab environment.
Furthermore, at the end of the course, it is expected from the student:
-with regards to understanding and knowledge: the student should
understand and show good command the models presented in the
course;
- with regards to applying knowledge and understanding: the student
should learn how to solve several practical problems;
- with regards to independent thinking: the student should show good
abilities in making judgements, developing line of reasoning as well as
expressing critical capacities;
- with regards to communication skills: the student should be able to
clearly and effectively
communicate what he/she has learned;
-with regards to learning skills: the student should update and
consolidate his/her quantitative knowledge and ba able relate this
knowledge to the other disciplines in the degree course.
Prerequisites
Matematica generale e finanziaria.
Course unit content
Introduction to probability. Random numbers: continuous and discrete. Random vectors. Probability distributions: uniform distribution, normal distribution and Student's t distribution. Portfolio selection: The mean-variance model. Value at risk.
Full programme
Elements of financial mathematics: discount factor, present value, evaluation of financial flows and the duration. Introduction to probability. Classical approach, frequentist,
subjective. Axiomatic approach. Space of results. Random events. Axioms of probability. Conditional probability. Bayes theorem.
Random numbers: measurability. Repartition function. Discrete random numbers, probability function. Continuous random numbers, probability density function. Expected value, variance and standard deviation. Random vectors. Stochastically independent random numbers. Covariance and correlation between two random numbers. Probability distributions: uniform distribution, normal distribution and Student's t distribution. Portfolio selection: the mean-variance principle. The Markowitz model. Value at risk.
Bibliography
Cesarone, F. (2020). Computational Finance: MATLAB® Oriented Modeling. Routledge.
E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Probability. A Brief Introduction, 2° edizione, Egea,
2009
Leaerning material provided during the course.
Teaching methods
Lectures. The theoretical contents of the course will be presented
rigorously. They will be accompanied by a wide discussion of examples
and exercises to be solved using Matlab software. To solicit the
participation of the students, they will be asked to solve these exercises.
Assessment methods and criteria
The exam consists of numerical exercises in Matlab. Learning skills and knowledge will be ascertained with a problem worth 30 points structured in seven questions.
The exercises proposed during the exam will be inspired by those presented during the lessons.
The duration of the exam is 90 minutes.
The evaluation of the exam is expressed out of thirty (scale 0-30), the minimum grade to consider the exam passed is 18 and the maximum mark is 30.
The text of the final exam with the relative solution will be uploaded to Elly within one week from the performance of the test. The test assessment will be posted on Elly within 10 days of taking the exam. For the rules on the attribution of the final grade and honors, please refer to syllabus of the entire course.
Other information
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2030 agenda goals for sustainable development
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