First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063747, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC2095, Degree course structure A.Y. 2014/15, A.Y. 2019/20
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination FINANCIAL MATHEMATICS
Website of the academic structure
Department of reference Department of Statistical Sciences
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ADILA MAGRIS
Other lecturers ELENA SARTORI SECS-S/06

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines SECS-S/06 Mathematics for Economics, Actuarial Studies and Finance 9.0

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 9.0 64 161.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
4 Commissione a.a. 2019/20 01/10/2019 30/09/2020 MAGRIS ADILA (Presidente)
CESARONI ANNALISA (Membro Effettivo)
SARTORI ELENA (Membro Effettivo)

Prerequisites: Properties of continuous and derivable functions, sequences and series, linear algebra.
Target skills and knowledge: At the end of the course students will know:
Simple interest rate, compound interest rate, accumulation factor, compound interests, annuities: net present value and future value in the case of constant installments, perpetuities, annuity-immediate, annuity-due. Amortization schedules: principal, interest, principal repayment, balance. Choice between financial operations: Net Present Value criterion, Interest Rate of Return criterion.
Bonds: zero coupon bonds: face value, maturity date, simple/compound return, trading return, taxation. Coupon bonds, coupon rate, yield to maturity, dirty price, clean price, accrued interest, issuance price, risk of default.
Term structure: yield curve, rate curve: coupon bonds like zero coupon bonds portfolio, unitary price structure; complete and incomplete markets: superfluous bonds, no-arbitrage price.
Macaulay duration, its properties, portfolio duration, bond duration; Macaulay convexity, efficient portfolio, assets and liabilities, Redington theorem, Fisher Weil theorem.
Spot and forward rate: forward rate implicit on spot rates.
Markowitz Theory: expected value, variance, stock portfolio, share expected return, share volatility, portfolio expected return, portfolio volatility, diversification effects, efficient portfolios, matrix notation, minimum variance portfolio, feasible set, efficient frontier, portfolio without short-selling.
Capital Asset Pricing Model: capital market line, tangent portfolio, market portfolio: basic comments.
Insurance, biomedical functions; life insurance: whole life insurance, term insurance. Pure endowments, endowment insurance.
Examination methods: Written exam.
Assessment criteria: The arguments of the exam exercises are the following:
Simple / compounding accumulation and discount, Annuities, Amortization schedule, Internal Rate of Return, Net Present value, profit index, Interest rate swap, Bonds, Spot and forward rates, Financial Immunization, Expected return, variance, minimum variance portfolio, Capital asset pricing model, Life insurance, Net premiums.
Course unit contents: Simple and compound interest. Bonds, interest rate structure, portfolio theory, life insurance.
Planned learning activities and teaching methods: Lessons in front of the class: in these lessons the teacher will explain the theory and the exercises of the mathematics concerning the financial aspects listed above. In these lessons exercises included in the exam session will be discussed.
Every week, on the Moodle platform, exercises will be proposed to the students to practice their knowledge on the arguments developed during the lessons. These exercises, some of these with automatic correction, will give to the student immediate information on her/his preparation level.
Some of these exercises will be proposed in flipped classroom modality, then the teacher or the students themselves will do them during the lessons, in this way the theory development will be facilitated using the technique of problem solving.
Additional notes about suggested reading: The writtten notes, the .pdf and the .xls slides used during the lessons will be uploaded on the Moodle platform: students will be able to use them without restrictions.
Every lesson proposed using digital ink will be uploaded on the Moodle platform in the .pdf format.
If in the classroom the teacher can record the lessons (on mp3 format or video format), these recorded lessons will be uploaded on the Moodle platform or on another appropriate available support.
Textbooks (and optional supplementary readings)
  • Elisabetta Allevi, Gianni Bosi, Rossana Riccardi, Magalì Zuanon, Matematica Finanziaria e Attuariale. --: Pearson, 2017.
  • David Lovelock, Marilou Mandel, A. Larry Wright, An Introduction to the Mathematics of Money. --: Springer, 2007.

Innovative teaching methods: Teaching and learning strategies
  • Flipped classroom
  • Auto correcting quizzes or tests for periodic feedback or exams
  • Active quizzes for Concept Verification Tests and class discussions
  • Video shooting made by the teacher/the students
  • Loading of files and pages (web pages, Moodle, ...)
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Kaltura (desktop video shooting, file loading on MyMedia Unipd)
  • Latex
  • Excel

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