30063  MATEMATICA  MODULO 2 (APPLICATA) / MATHEMATICS  MODULE 2 (APPLIED)
Department of Decision Sciences
For the instruction language of the course see class group/s below
MARGHERITA CIGOLA
Class group/s taught in English
Classgroup lessons delivered on campus
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
 Integral calculus: antiderivative; indefinite integral; integration methods; definite integral; integral function; generalized integrals and convergence criteria.
 Probability Calculus: classical, empirical and subjective approaches. Axiomatic approach: sample space, events algebra, probability measure. Conditional probability.
 Random numbers and vectors: distribution function, probability and probability density functions. Expected value and variance of a random number. Joint and marginal probability function of a random vector; stochastic independence and linear correlation; covariance; expected value and variance of a linear combination of random numbers.
 Financial calculus: present and final value: financial laws of one and two variables. Decomposability. Annuities and loan amortization. Consumer credit.
 Fixed income bonds. Interest Rate Term Structure. Duration: financial immunization and volatility of the bond price.
 Financial choices: DCF, NPV and IRR. Generalizations: GNPV, APV and GAPV. Financial leverage. Decomposition of global indices.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
 Recognize the proper meaning of standard indices of cost/profitability for a financial operation such as NPV, IRR, etc..
 Identify the proper meaning of probabilistic statements and terms concerning random quantities such as uncorrelated random yields, default risk and so on.
 Reproduce the correct procedures for computing integrals, probabilities and financial quantities.
APPLYING KNOWLEDGE AND UNDERSTANDING
 Apply the learned calculus methods to compute and/or asses the correctness of quantities which are relevant both in theory and in practice such as: the no arbitrage price of a bullet bond, the internal effective rate of a loan, the expected returns rate of a portfolio, etc..
 Evaluate the profitability of a financial operation by choosing the proper method/model to adopt.
 Compute a probability measure that is coherent with the available information on the stochastic event/number.
Teaching methods
 Facetoface lectures
 Online lectures
 Exercises (exercises, database, software etc.)
DETAILS
Teaching and learning activities for this course are divided into (1) facetoface and/or online lectures, (2) in class and/or online exercises (3) selfassessment online materials.
 During the lectures convenient examples and applications allow students to identify the quantitative patterns and their main logicalmathematical properties.
 The in class exercises allow students to apply the analytical tools illustrated during the course.
 Besides the exercises proposed in class, further exercises, such as "mock exams" and "past written exam" are uploaded online. The online exercises allow students to individually practice and selfassess their own skills.
Assessment methods
Continuous assessment  Partial exams  General exam  


x  x 
ATTENDING AND NOT ATTENDING STUDENTS
The exam modality is written: the final grade depends exclusively on the student performance in the written exam.
The written exams consist of both closedanswer and openanswer questions. Their structure is designed in order to assess:
 The ability to identify the convenient mathematical tool to be used in the described context.
 The ability to correctly apply the chosen tool to compute the required result.
 The ability to properly understand the meaning of the learned notions and models
 The ability to recognize the main properties and the related logical connections of the main learned notions.
Every student may take one general exam which is worth the 100% of the final grade. Alternatively students may take two partial written exams (midterm and endterm exams). In such a case each partial exam is worth 50% of final grade.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
Textbooks:
 L. PECCATI, S. SALSA, A. SQUELLATI, Integral Calculus, Extract from Mathematics for Economics and Business, Milano, EGEA, 2008 (Chapter 7).
 E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Probability. A Brief Introduction, Milano, EGEA, 2009, second edition.
 E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Financial Calculus with Applications, Milano, EGEA, 2013.
Further materials will be distributed on Blackboard platform at the beginning of the course.