Luiss

Mathematical Methods for Finance, 2021-22

HOT NEWS

(3)

Supplementary face-to face Office Hours of Prof. Fausto Gozzi:

Friday 22 October 2021 h. 14.30-16: face-to face in office 517.

 

(2)

In the next three Wednesdays: October, 13, October 20 and October 27

there will be additional TA Sessions online given by Dr. Antonio Veredice:

Time and Room:

08:00 – 09:30, Virtual Room 62

 

(1)

Supplementary Office Hours of Prof. Fausto Gozzi:

Saturday, October 9, h 10-11, online (Microsoft Teams)

 

WELCOME TO THE WEBSITE OF THE COURSE “MATHEMATICAL METHODS FOR FINANCE 2021-2022”

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IMPORTANT NOTICE

The course has changed its title and structure. Hence we invite all students, in particular those who are not of the first year, to check carefully the new rules.

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In this page you can find, beyond all up-to-date news about the course (which are given above in inverse chronological order under the title “Hot News”), the following material.

(A) Teachers and time table

(B) Precourse, self-evaluation test and tutoring

(C) Office hours and forums

(D) Textbooks

(E) Preliminary program and effective one

(F) Exam rules

(G) The material for the first part of the course

(H) The material for the second part of the course

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(A) Teachers and time table.

Teacher: prof. Fausto Gozzi;

Assistants: dr.ssa Giulia Pisegna and dr. Mattia Scandolo;

The course starts Monday, September 20 and ends Friday, December 3 with the following schedule:

Monday 9-10.30 (online room 38)

Tuesday 10.45-12.15  (online room 70)

Thursday 9-10.30  (online room 61)

Friday  (face-to-face): Group 1, 9.45-11-15; Group 2, 11.30-13.

Supplementary hour online: Wednesday 8-9.30. Sometimes it may be used for recovery. In such case there will be a notice in the website of the course.

The course “Lab of software application for finance” will teach you how to use some software to solve some of the mathematical problems which you will encounter in this course. The teacher of such course is Prof. Anna Maria D’Arcangelis. Information about this course can be found at the web page of such course.

 

(B) Precourse, self-evaluation test and tutoring.

The course starts giving for granted the basic arguments (one variable calculus and basic linear algebra) taught at the standard mathematics courses of the italian “laurea triennale” in economics and similar subjects. It is our experience that some students may not remember well such topics, as in many cases they studied mathematics only the first year, while mathematics is a skill that needs to be trained frequently.

Till last year the University has provided a precourse (with a teacher) summarizing part of the basic arguments needed to be able to understand the lectures of the course. This year the precourse has not been organized (hence there is no teacher for it) but the material of the precourse of the previous year is still online and the students are invited to look at the precourse material online at this site:

https://learn.luiss.it/course/view.php?id=1814

It is compulsory for all students to study the precourse material (unless they perfectly remember all the topics treated there). It is also compulsory to take the final self-evaluation test of the precourse. The students who get a grade strictly less than 18 in the self-evaluation test must contact TAs to agree about a recovery plan that can help them to understand the course.

Office hours and forums

The office hours below are valid only during the course (i.e. from September 20, 2021 till December 3 2021). After the course the office hours will be only by appointment (to agree personally or by email). During the course it is always possible to ask questions after the lectures and/or request supplementary office hours by email. In some cases office hours will be advertised in the section “Hot News” at the beginning of this web page.

Professor: Fausto Gozzi. Wednesday h.8.00-9.00 (online over Microsoft Teams or other platforms). Email: fgozzi at luiss dot it.

Assistants.
Giulia Pisegna: Monday 17-18. Email: giulia.pisegna@uniroma1.it

Mattia Scandolo: Tuesday 15-16. Email: mattia.scandolo@uniroma1.it

To interact with the professor and the assistants and/or among them, the students can also use the forums which are activated on the page of this course on the luiss learn website. Every student can post and/or ask questions on the general forum. This should be the standard way to ask questions about the course. Of course, for private questions, the students should use the email.

(D) Textbooks

Main textbook
Authors: Simon, Blume,
Title: Mathematics for economists
Editor: Norton

Other textbooks

Authors: Lawrence E. Spence, Arnold J. Insel, Stephen H. Friedberg Title: Elementary Linear Algebra
Editor: Pearson Education

Author: James Stewart
Title: Calculus (International Metric Edition)
Editor: Brooks/Cole; International Edition

Author: Michael C. Delfour
Title: Introduction to Optimization and Differential Calculus
Editor: SIAM

Autori: C. Pocci, G. Rotundo, R. de Kok
MATLAB for economics ans financial applications.
Maggioli Editore, 2016.

(E) Preliminary program and effective one

Here is the line to the preliminary program published on the Luiss site:

https://www.luiss.it/cattedreonline/corso/M433/0/19FLMF1/2021

Final program of the same course of last year

NewContentofLecturesENGECFINFall2020

The program for this year will be different for the two majors and it will be posted here after the course.

Here you find the content of lectures, together with references, updated every 1-2 weeks

Week1ContentofLecturesENGECFINFall2021

Week2ContentofLecturesENGECFINFall2021

Week3ContentofLecturesENGECFINFall2021

Week4ContentofLecturesENGECFINFall2021

 

(F) Exams rules

There will be no mid term exam.

The exam consists of a written test and an oral test. The written test must be carried out face-to-face. If, due to the COVID emergency, this will not be possible, then the written test will not take place and the exam will consist only of the oral test.
The exam program consists of two parts: the first part (P1) concerns basic topics with some basic applications; the second (P2) concerns slightly less basic topics and some more applied models. Students can decide to take only the first part (P1) and in this case the final grade will be a maximum of 25.
There is a two-point bonus for those who, enrolled at the academic year 2021-22, take the exam within the February session.
For those who take the exam only on the first part, if the grade plus the bonus is greater than 25, the student can only register 25.
Part of the course, as emphasized in the content of lectures, is called “optional” in the following sense:
1) Students that wants to get a degree less or equal to 28 can avoid studying this part and will not receive questions about it. The degree will be at most 28 (included the bonus).
2) Students that wants to get a degree possibly more than 28 must study this part and will receive one or more questions about it. The the degree may be more than 28.
If a student does not answer correctly to at least one question of the optional part, the grade cannot be more than 28, including the bonus.

(i) The case in which it is possible to carry out written tests face-to-face.
The student who has achieved a sufficient mark in the written test can choose to:

a) record the grade (without taking the oral exam);
b) take the oral exam.

In case a) the maximum grade that can be recorded is 25 (therefore a student with a grade higher than 25 in the written test who decides not to take the oral exam could record a maximum of 25).

Important note. In this case the choice to register the grade without taking the oral exam must be validated by the professor. For some students the professor may decide that the oral exam is needed in any case.
If the student decides to take the oral exam (case b)), the final mark, expressed out of thirty (X / 30), will depend on the combined result of the two tests, and therefore may be higher or lower than the mark of the written test. The student may also be rejected (regardless of the grade of the written exam) if the oral exam is seriously insufficient. In this case, the student will have to repeat the written test in a subsequent exam.
The questions proposed in the oral exam concern both theory topics and practical exercises.
A sufficient grade obtained in the written test is maintained until the last useful exam session of the current academic year and no later than that date (without any exception). Therefore, it is possible to plan any oral exam in a subsequent session with respect to the one in which the written exam was taken, as long as it relates to the same academic year.
The student has the right to refuse the grade of the written test and/or the oral test. The refusal of the grade obtained in the oral test entails the need to take the written test again in any of the subsequent sessions foreseen in the exam calendar.
About the written test (if any).

The written test may include theory questions and is completely “closed-book”: it is not allowed to consult books and / or notes and the use of electronic devices of any kind is not allowed. People using any of such devices or violating rules will be carefully prosecuted.

The written test can be repeated at each available date but every delivery cancels the previous grades. The oral exam (or the registration) can be done at every available date (but in the same academic year), not necessarily the same of the written exam. 


(ii) The case when it is NOT possible to carry out written tests face-to-face.
The exam will be oral only and will necessarily take place online.
The student must communicate whether she/he intends to carry out the oral exam on the whole program or only on the first part (P1).
In case of oral only on the first part, the maximum achievable mark will be 25.
In the event of an oral on both sides, the vote will have no restrictions (neither upwards nor downwards).
If a student takes the oral exam on the first part and refuses the grade, she will then have to repeat the exam.

 

The written test can be repeated at each available date but every delivery cancels the previous grades. The oral exam (or the registration) can be done at every available date (but in the same academic year), not necessarily the same of the written exam.

The oral exam cancels all the previous written/oral tests. Hence if a student does not take the vote of the oral exam she has to repeat the exam.

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(G) The material for the first part of the course

(G1) Slides

Week 1 (Sept. 20-24)

Week1SlidesFGMethodsFirstPartFallFIN2021

Monday20SeptSlidesFGMethodsFirstPartFallFIN2021

Tuesday21SeptSlidesFGMethodsFirstPartFallFIN2021

Thursday23SeptSlidesFGMethodsFirstPartFallFIN2021

Friday24SeptWhiteboardFGMethodsFirstPartFallFIN2021Group1

Friday24SeptWhiteboardFGMethodsFirstPartFallFIN2021Group2

 

 

Week 2 (Sept. 27-Oct. 1)

Week2SlidesFGMethodsFirstPartFallFIN2021

Monday27SeptSlidesFGMethodsFirstPartFallFIN2021

Tuesday28SeptSlidesFGMethodsFirstPartFallFIN2021

Thursday30SeptSlidesFGMethodsFirstPartFallFIN2021

 

Week 3 (Oct. 4-8)

Week3SlidesFGMethodsFirstPartFallFIN2021

MondayOct4Week3SlidesFGMethodsFirstPartFallFIN2021

Tuesday5OctWeek3SlidesFGMethodsFirstPartFallFIN2021

Thursday7OctWeek3SlidesFGMethodsFirstPartFallFIN2021

 

Week 4 (Oct. 11-15)

Week4SlidesFGMethodsFirstPartFallFIN2021

Monday11OctWeek4SlidesFGMethodsFirstPartFallFIN2021

Tuesday12OctWeek4SlidesFGMethodsFirstPartFallFIN2021

Thursday14OctWeek4SlidesFGMethodsFirstPartFallFIN2021

 

Week 5 (Oct. 18-22)

Week5-6-7FINLecturesFG2020LinOpSpectrum

Tuesday19OctWeek5-6-7FINLecturesFG2020LinOpSpectrum

 

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(G2) Tutorials

Tutorial1part1MMEF2021FG

SolutionsTutorial1part1MMEF2021FG

 

Tutorial2MMEFfall2021FGJacobianIFT

SolutionTutorial2MMEFfall2021FGJacobianIFT

 

Tutorial3MMEFfall2021UnconstrainedOptimization

SolutionsTutorial3MMEFfall2021UnconstrainedOptimization

 

Tutorial4MMEFConstrainedOptimization1EqualityFall2021

SolutionsTutorial4MMEFConstrainedOptimization1EqualityFall2021

 

Tutorial5MMEFcomplexnumbersWithSolutions

 

Tutorial6MMEF2021BasicLinearAlgebra

 

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(G3) TA sessions

TA1_Sets_parametricLines

TA2_Jacobian_IFT

TA3_ConstrOpt

Complex_Numbers_Slides

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(G4) More material on the first part (seminars, answer to interesting students’ questions, etc)

This material is optional (i.e. it can be asked to students that aim to get a grade bigger than 28)

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(H) The material for the second part of the course

(H1) Slides

 

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(H2) Tutorials

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(H3) TA Sessions

_______________________________________________________________________

(H4) More material on the second part (seminars, answer to interesting students’ questions, etc)

This material is optional (i.e. it can be asked to students that aim to get a grade bigger than 28)

 

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