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
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
- Face-to-face lectures
- Online lectures
- Exercises (exercises, database, software etc.)
DETAILS
Teaching and learning activities for this course are divided into (1) face-to-face and/or online lectures, (2) in class and/or online exercises (3) self-assessment online materials.
- During the lectures convenient examples and applications allow students to identify the quantitative patterns and their main logical-mathematical 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 self-assess their own skills.
Assessment methods
Continuous assessment | Partial exams | General exam | |
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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 closed-answer and open-answer 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 (mid-term and end-term 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.