Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Primo semestre Magistrali dal Sep 26, 2016 al Jan 13, 2017.
The course aims to introduce the main methods and quantitative models to support the management and businesses in international markets, within certain and uncertain
In particular, the main quantitative applications will be thoroughly analyzed for the company's performance, customer relations, market and sector situation, financial planning and insolvency risk.
The course is divided into parts in each of which it is introduced a quantitative model and are then proposed applications to specific business contexts.
At the end of the course, the student will be able to apply the principal models seen in order to complement the other skills with a quantitative support for the critical analysis and interpretation of the business trend and the financial reference scenario.
Recalls metric and topology. Functions of several variables: domain, graphic, level surfaces, limits and continuity. Partial derivatives. Differentiability, continuity and tangent plane. Linear functions and quadratic forms.
Differential of functions of several variables and mean value theorem to analyze the components of revenue and margin business and their variations.
Differential and mean value theorem for functions of several variables. Application to the analysis of changes in the components of the turnover. Application to the analysis of changes in the components of the margin.
Analysis of the relative frequencies and matrices of representation for the evaluation of customer loyalty business.
Analysis of the relative frequency of events and matrices of representation. A model for the analysis of company customers for product class. Steady-state conditions. Retention indices. Application analysis of customer loyalty. Application analysis of customer loyalty by sales class.
Linear dynamic systems for assessing market shares.
Systems of linear homogeneous difference equations of the first order. Solutions and equilibrium points. Application to the dynamics of the transition of customers from brand to brand for homogeneous products. Application to the dynamics of the transition of clients between substitutes.
Analysis of the relative cumulative frequencies and Lorenz curve for the evaluation of the concentration of customers and the company's turnover.
Cumulative frequencies related and Lorenz curve for the analysis of the concentration of a quantitative character. Concentration Index. Application analysis of the concentration of sales. Application analysis of the concentration by turnover.
Dynamic systems for the construction and economic financial analysis of a business plan.
Systems of finite difference equations of first and second order. Vector representation. Application to the representation of the dynamics in time of economic flows, financial, equity and profit for the year. Application to the construction of a business plan.
VaR and financial ratios for the risk assessment of corporate insolvency.
Default Point, Expected Value and Standard Deviation, Distance to Default Point expressed in number of Standard Deviations, Value at Risk and Probability of Default. Application to the value of company activities and assessment of the risk of insolvency.
Linear programming problems and business applications.
Linear programming problems. Graphical method. Simplex method and use of the software JavaSimplex to the search for a solution. Sensitivity analysis, interpretation and economic shadow prices. Solutions to integer values. Leading business applications: optimization of product mix, optimize the combination of factors of production (problem of the diet), transport optimization, optimization of rounds, optimization of campaigns.
Reticular programming Techniques, PERT and CPM, for the building of projects.
Graph Theory. Path problems and good flow. . P.E.R.T. and C.P.M. deterministic and stochastic: time, resources, costs. Application to the construction of a company project.
Handouts, notes and teaching material available online through the e-learning course page.
E. CASTAGNOLI, L. PECCATI, La Matematica in azienda: strumenti e modelli. Volume II: sistemi lineari. Volume III: Calcolo differenziale con applicazioni. Volume IV: Sistemi dinamici, EGEA Bocconi, Milano 2003.
M. FISCHETTI, Lezioni di Ricerca Operativa, II edizione, Libreria Progetto, Padova 1999.
F.S. HILLIER, G.J. LIEBERMAN, Introduction to Operations Research, McGraw-Hill, 9th edition 2012.
R.E. MARKLAND, Topics in Management Science, J. Wiley & Sons, 1989.
P.A. JENSEN, J.F. BARD, Operations Research: Models and Methods, John Wiley and Sons, 2003.
The conduct of the lessons.
The course consists of 54 hours of lectures, that develop applications and simulations.
There are also the hours devoted to the preparation of the project work.
To access the exam, the student must first develop a project work that will have to get a positive evaluation of the teacher.
The project work will be developed, with the help and under the supervision of the teacher, in study groups of up to 4 students that will have to make application and/or insights of the techniques, models and methods developed and produce a written, The Project Work, to be sent to the teacher via e-mail, for evaluation.
The project work is part of the methods of active participation of students in the course and is introduced with the aim of:
- Stimulate the student to the coordination and use of various instruments designed for operational purposes;
- Improve the capacity and quality of interpersonal relationships and in particular the work in teams;
- Improve the capacity and quality of presentation/display using patterns and vocabulary typical of the asset management.
The exam consists of a written test on all the topics in the program, designed to test the knowledge gained.
The commission may request an oral evaluation aimed to further verify the mastery of knowledge acquired in connection with the use of operational cases.