Educational objectives The course aims at enabling students to grasp the basic mathematical topics and tools needed in Economics and Firm Management modelling, such as linear algebra, multivariable functions, static optimization methods, and techniques to solve differential equations.
Students that pass the exam will be able to handle quadratic forms, to study their sign, to diagonalize matrices, to work with multivariable functions, such as utility and production functions, to optimize functionals depending on them, with or without constraints, to calculate Lagrange multipliers, and to solve differential equations.
The course requires a good knowledge of basic mathematics and financial mathematics acquired in three-year degree courses; it is closely related to the course of Probability and Stochastic Processes and provides the basis for the subsequent teachings of Risk Theory, Quantitative finance, Methods and models for finance, Times series, Actuarial mathematics for the private companies of the same course graduation.
Knowledge and understanding: After attending the course, students will be able to know the evaluation procedures of financial problems and to understand the results of mathematical models used to resolve those problems.
Ability to apply knowledge and comprehension: At the end of the course, students will be able to use basic mathematical tools to evaluate financial problems in accordance with any robust financial theory and to apply a right knowledge in their use to real evaluation problems.
Judgment skills: At the end of the course students will be able to understand the results derived from the financial tools applied and to explain differences among figures obtained from different models, in relation to the theoretical setting in wich the evaluation is provided.
Communication skills: After passing the exam, students will be able to explain and discuss about the arguments treated during the course, giving their comments and remarks on the use of the mathematical tools learnt.
Self-learning skills: After passing the exam, students will have a knowledge of the advanced mathematical topics and tools for financial modelling that will permit them to face future studies in mathematical finance for pricing of liquid and illiquid financial instruments.
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Educational objectives The main goal of the course is to provide students with a fair knowledge of the fundamental concepts of modern probability theory and of the most elementary stochastic processes, such as Markov Chains and Poisson Processes, through rigorous definitions of the main concepts and proofs of the most important theorems.
The student should be able to i) understand and explain concepts, ii) connect and compare the main ideas, iii) be able to prove the fundamental theorems.
He will also be able to solve problems and to model real situations according to examples shown in class.
Many problems in probability may be solved in different ways. This allows to consider different approaches and discuss together relations among them in order to understand and correct potential mistakes.
This course is fundamental to properly take more advanced courses in Mathematical Finance, Statistical Inference, Risk Theory and Time Series Analysis.
Specific goals
1) Knowledge and understanding. Upon completion of the course, the student will be able to use the basic tools of probability necessary for understanding the main stochastic processes. He will therefore have a clear understanding of the concepts of dependence and independence of random phenomena and their long-term trends. The student will also be able to distinguish between processes that operate in continuous and discrete time. Furthermore, the study of Markov chains and their limit distributions will allow the student to understand the problems related to discrete-time stochastic processes.
2)Ability to apply knowledge and understanding. Through the theoretical and practical knowledge of the main models used in probability theory and in stochastic processes, the student will be able to understand the dynamics of financial phenomena by interpreting their characteristics in the best possible way.
3) Autonomy of judgment. Through the solution of probability exercises, the student will be able to autonomously identify the models suitable for describing various financial phenomena. She/he will also be able to analytically calculate the main parameters associated with these models by correctly interpreting their meaning
4) Communication skills. To handle the probabilistic concepts of this course, the student must get used to expressing himself rigorously, correctly formalizing intuitions and managing to express them in oral and written form. For this purpose, the teacher will stimulate interaction with students both during practical exercises and in the presentation and demonstration of the main theoretical results of the course
5) Learning skills. The analytical tools and theoretical models developed during the course will give the student the necessary skills for an analytical approach to the use of any predictive and explanatory model to be used in the financial field. In addition, the student will also have the ability to correctly evaluate the uncertainty associated with the forecasts made through statistical and econometric models
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Educational objectives The main methodologies of corporate valuation are analyzed and the approaches commonly used by practitioners (financial analysts, investment and merchant banks, consulting firms) are critically discussed. Examples will focus on corporate valuation issues using DCF, stock market and deal multiples completed by industry-specific as well as case-specific valuation techniques.
Students who have passed the examination will be able to analyze the conceptual and theoretical framework surrounding valuation issues and the practical tools to address such topics in real-life situations.
Students who have passed the examination will acquire the skills to pass the tests certification to practice as a chartered accountant and to play activity of counselling of professional accountancy.
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Educational objectives The course aims to provide students with a systematic introduction to the R software with particular attention to aspects related to the simulation of random variables and stochastic processes. During the course the Monte Carlo method for the numerical computation of integrals will also be introduced.
The student should be able to use the R software to replicate the main theoretical probability results such as the law of large numbers or the central limit theorem through simulations. She/he will also be able to simulate the trajectories of some stochastic processes both in discrete time (random walks or more generally Markov chains) and in continuous time (Poisson process). In this way, the student will be able to have a greater perception of the theoretical characteristics related to the modeling of random phenomena and at the same time will have a solid knowledge of programming in R
The Computer Probability course will provide indispensable tools to successfully follow, in addition to the Probability and Stochastic Processes course, also the Time Series Analysis course and more gener-ally any quantitative course.
Specific goals
1) Knowledge and understanding. Upon completion of the course, the student will be able to use the basic R commands to synthesize and graphically represent data sets. The student will also be able to use R commands for the simulation of the main random variables and will be able to program short codes for the simulation of both non-standard random variables and random processes.
2) Ability to apply knowledge and understanding. Through the theoretical and practical knowledge of the simulation of the main models used in probability and in stochastic processes, the student will be able to understand the dynamics of financial phenomena by interpreting their characteristics in the best possible way.
3) Autonomy of judgment. Through the solution through simulation techniques of probability exercis-es, the student will be able to independently identify the models suitable for describing various ran-dom phenomena of a financial nature. She/he will also be able to numerically calculate the main pa-rameters associated with these models by correctly interpreting their meaning
4) Communication skills. To handle both the concepts related to R programming and the probabilistic ones, the student must get used to expressing himself rigorously, correctly formalizing intuitions and being able to express them in oral and written form. For this purpose, all the lessons will be held in the computer labs, and the teacher will continuously stimulate interaction with the students
5) Learning skills. The programming tools and probabilistic models developed during the course will give the student the necessary skills for an analytical approach to the use of any predictive and ex-planatory model applied in the financial field. In addition, the student will also have the ability to cor-rectly assess the uncertainty associated with the forecasts made through statistical and econometric-financial models
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Educational objectives The course aims at showing, both from a graphical point of view and from a methodological one, the main tools for analyzing economic and financial time series. Students will also learn to use to the statistical software R as a tool for applying statistical methodologies to real data, as well as for understanding the theory behind a model.
Students who pass the exam will know the main concepts and procedures for model building when analyzing economic and financial time series.
Students who pass the exam will have skills for data analysis: on the basis of the methodologies introduced in the course and of the knowledge of the R software tools, they will be able to choose the best model to represent real economic and financial phenomena. Starting from real data they will be able to find the best strategy to represent data.
They will also be able to analyze in a critical way the obtained results, highlighting pros and cons of the chosen procedures. Students’ skills are stimulated by tackling real case studies and developing a research project which will be discussed in class. The evaluation of the report will also concern students’ communication skills and their ability to explain what they learned and the results of the quantitative analysis.
The deep comprehension of the learned methodologies, will allow the student to understand more general models not explained in the course, evaluating advantages and disadvantages.
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Educational objectives The course aims to provide students with basic knowledge and tools on the cognitive functioning of the financial system through analysis of its international attitude and development. In particular, the course analyses all the components that characterize the operation of financial intermediaries upon different financial systems, distinguishing between different countries’ systems of regulation and supervision.
At the end of the course student will be able to perform comparative analysis of different financial systems in terms of business models, types of institutions, organization of capital markets. In particular
• Knowledge and understanding: at the end of the course students will have the knowledge base of the fundamentals elements for the effectiveness of financial system and its functioning in an international perspective;
• Applying knowledge and understanding: students will have the knowledge of and some skill in the way in which truth-finding and the development of theories and models take place in the relevant fields of international financial systems;
• Making judgements: students will have the knowledge of and some skill in the way in which decision-making takes place in the relevant fields, in order to improve any enhancement on the functioning of international financial systems;
• Learning skills: Has knowledge of and some skill in the way financial systems can satisfy the issues coming from the economic units
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Educational objectives The goal of this course is to describe the main pricing methodologies for financial instruments, when the underlyings are governed by either discrete-time and continuous-time stochastic processes, with particular emphasis on the Black-Scholes-Merton model. Moreover, the course provides computational tools for pricing and hedging. The main topics will be introduced from a theoretical perspective. Furthermore, they will be analyzed from a computational point of view, using MATLAB software.
• (Knowledge and understanding) At the end of the course, students will be able to apply the main numerical methodologies for financial derivatives pricing, both in discrete-time and continuous-time diffusion market models. They will also be able to understand and illustrate the main characteristics of each numerical method and to recognize the most effective solution to the economic-financial problem they will face. Finally, they will manage to apply the theoretical framework to practical experiences, in order to obtain the fair value of derivative securities.
• (Applying knowledge and understanding) The students who pass the exam can identify the suitable model to describe the financial structure, and also establish the most efficient methodologies to solve the related financial issues.
• (Making judgements) By using the information inferred from the lectures, students autonomously may inspect the financial context, take into account the whole range of methods to use, and interpret the obtained results.
• (Communication skills) After passing the exam (that consists of a written/practical text with open-ended questions and/or exercises and/or practical works with Matlab), students will be able to adequately outline the main topics covered by the lectures, either verbally or through written documents.
• (Learning skills) Standard lectures, lab activities and self-study allow students to develop a method to autonomously acquire new financial knowledge and theoretical\practical skills.
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