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MATHEMATICS FOR FINANCE
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MATHEMATICS FOR FINANCE
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Academic year 2021/2022
- Course ID
- SEM0065
- Teaching staff
- Tiziano De Angelis (Lecturer)
Bertrand Lods (Lecturer) - Degree course
- Finance
Insurance and Statistics - Year
- 1st year
- Teaching period
- First semester
- Type
- Distinctive
- Credits/Recognition
- 12
- Course disciplinary sector (SSD)
- SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz.
- Delivery
- Blended
- Language
- English
- Attendance
- Optional
- Type of examination
- Written
- Prerequisites
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A good knowledge of basic calculus (Matematica Generale), of the foundations of probability calculus and statistical infererence (Statistica)
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Sommario del corso
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Course objectives
This course is aimed at introducing and developing many of the mathematical tools which are used in applied finance and insurance. ln this module, particular stress will be posed on the development of the measure theoretical tools and advanced probability concepts with emphasis on their applications to investment and insurance decisions. The introduction of stochastic processes and their properties is always motivated by the wish to develop models for observed phenomena.- Oggetto:
Results of learning outcomes
At the end of the course, the student is expected to be capable of:- using the basic tools and results to pose, formalize and solve a probability problem of applied interest
- knowing the extent to which the results obtained in the previous step are dependent on the assumption that s/he has made about the behaviour of the economic agents
- being able to think about possible and useful generalizations of the model
- being able to communicate such findings using appropriate and clear mathematical notation and language
- applying the basic course knowledge to theoretical issues and situations
- approaching the subject in a critical manner through the examination of different approaches in the literature and practice of mathematical finance
- having gained communication skills, through class discussion
- having gained learning abilities, through a variety of learning tools (teaching material, class discussion, lab sessions, homeworks and tests)
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Course delivery
The course is articulated in 96 hours of formal in-class lecture time, and in at least as many hours of at-home work solving practical exercises.- Oggetto:
Learning assessment methods
The course grade is determined solely on the basis of a written examination. The examination tests the student's ability to do the following:- Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results
- Use effectively the concepts and the results to answer questions in basic measure theory and stochastic process theory, e.g., computing the Ito integral of some given stochastic process.
The above is accomplished by asking the student to answer open questions: 2-4 questions on part 1 (12.5 marks), 2-4 questions on part 2 (17.5 marks). Questions can be essay questions or exercises. The minimum exam grade is 18/30, the maximum grade is 30/30 cum laude. More details on the exam can be found on Moodle.
The exam is a closed-book exam lasting 2.5 hours. Use of calculators is not permitted.
The student can take the exam at most three times per academic year on a total of five exam sessions (December, January, February, June and September).
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Support activities
Short course on "Essentials of Mathematics" held in September.- Oggetto:
Program
The course is divided into two parts:Part 1 [48 hours]: Probability with martingales (De Angelis)
- Review of differential and integral calculus
- Introduction to measure spaces
- Events and random variables
- Independence
- Introduction to Lebesgue integrals
- Expectation and L^p spaces
- Product measure and Fubini’s theorem
- Conditional expectation
- Elements of martingale theory
- Applications: Black-Scholes model in discrete time
Part 2 [48 hours] : Stochastic Processes (De Angelis-Lods)
- Brownian motion
- Stochastic calculus
- Connection with PDEs
- Change of measure
- Introduction to jump processes
Suggested readings and bibliography
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The following are the required textbooks for the course:Part 1
- D. Williams (1991). Probability with Martingales. Cambridge University Press.
Part 2
- Shreve (2004). Stochastic calculus for finance II, Springer.
- Oksendal (2003). Stochastic differential equations: an introduction with applications, Springer
Books may be avaiable from the School library's online resources:
https://www.bem.unito.it/it/che-cosa-cerchi/ testi-desame-e-altri- materiali-didattici Testi consigliati:Part 1
- D. Williams (1991). Probability with Martingales. Cambridge University Press.
Part 2
- Shreve (2004). Stochastic calculus for finance II, Springer.
- Oksendal (2003). Stochastic differential equations: an introduction with applications, Springer
I testi potrebbero essere reperibili dall'archivio digitale della biblioteca:
https://www.bem.unito.it/it/che-cosa-cerchi/ testi-desame-e-altri- materiali-didattici - Oggetto:
Class schedule
Days Time Classroom Monday 11:00 - 14:00 Aula R. Corradetti - Edificio Storico (3° piano) Polo di Management ed Economia Thursday 13:00 - 16:00 Aula 10 - Edificio Storico (3° piano) Polo di Management ed Economia Friday 14:00 - 17:00 Aula R. Corradetti - Edificio Storico (3° piano) Polo di Management ed Economia Lessons: dal 20/09/2021 to 10/12/2021
Notes: Links to webex meetings for students attending classes remotely are provided on Moodle
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Note
The methods of teaching activity could change in according to the limitation imposed by the current health crisis.Le modalità di svolgimento dell'attività didattica potranno subire variazioni in base alle limitazioni imposte dalla crisi sanitaria in corso.- Oggetto:
