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NUMERICAL AND STATISTICAL METHODS FOR FINANCE

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NUMERICAL AND STATISTICAL METHODS FOR FINANCE

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Academic year 2016/2017

Course ID
ECO0152
Teaching staff
Prof. Stefano Favaro (Titolare del corso)
Raffaele Argiento (Titolare del corso)
Degree course
Finance
Insurance and Statistics
Year
1° anno
Teaching period
Primo semestre
Type
Caratterizzante
Credits/Recognition
12
Course disciplinary sector (SSD)
SECS-S/01 - statistica
Delivery
Tradizionale
Language
Inglese
Attendance
Facoltativa
Type of examination
Scritto
Prerequisites
Is very important for the students to be familiar with the basic topics in mathematics, probability and statistics acquired in the three-year undergraduate program. These topics are presented in the short course "Essentials of Mathematics and Probability" usually given in September: see www.masters-finins.unito.it/ for more details.
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Sommario del corso

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Course objectives

Ability to solve, through the use of simulation tools, some standard problems in probability and statistical inference. Ability to apply statistical concepts and statistical techniques with respect to the point estimation, hyphotesis testing and confidence sets. Ability to the code with the language R/Matlab and to use some of its main packages.

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Results of learning outcomes

Knowledge and understanding
Advances knowledge of statistical modeling via point estimation, hypothesis testing and confidence intervals; basic knowlegde of Monte Carlo simulation techniques for statistical models; basic knowlegde of the language R/Matlab.

Applying knowledge and understanding
Ability to convert various problems of practical interest into statistical models and make inference on it; ability to implement a Monte Carlo simulation of a statistical model using the language R/Matlab.

Making judgements
Students will be able to discern the different aspects of statistical modeling and of  Monte Carlo simulation with the language R/Matlab.

Communication skills
Students will properly use statistical and probabilistic language arising from the classical statistics and Monte Carlo simulation; students will properly use the language R/Matlab.

Learning skills
The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of statistical modeling and Monte Carlo simulation using the language R/Matlab.

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Course delivery

Main lectures are devoted to the theorerical aspects of statistical inference based on the likelihood function and Monte Carlo simulation. Exercises will be assigned during these lectures. Lecture devoted to exercises and practical sessions with the language R are included in the course.

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Learning assessment methods

With regards to statistics, the exam consists of two parts: the first part is a formal discussion of one of the main topics of statistical infence based on the likelihood function; the second part is an exercise, typically with more than two questions.

With regards to simulation, the exam consists of two parts: the first part is a written exam on theory; the second part is a practical session with R.

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Support activities

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Program

1. Statistics: The module deals with some key themes of the theory of statistical inference, with emphasis on the role of the likelihood function. Topics include

  • Random samples and their distributions, the statistical model, the likelihood function, exponential family.
  • Sufficient statistics and minimal sufficient statistics, finite properties for estimators, asymptotic properties for estimators, methods for evaluating estimators.
  • Methods for constructing point estimators: method of moments and generalizations, method of the least square errors, method of maximum likelihood, methods of minimum distance. 
  • Hypothesis testing: probabilistic structure of hypothesis testing, Neyman-Pearson lemma, likelihood ration tests, asymptotic tests, confidence sets.

2 Simulation: this module aims at introducing the students with computational statistics methods. The program includes some computationally intensive methods in statistics, such as Monte Carlo methods, bootstrap, and permutation tests. An important part of the module will be devoted to practicals. All the methods discussed during the course will be will be implemented in the R software.

Topics includes:

  • Pseudo-random number generator. Linear congruential generators.
  • Methods for Generating Random Variables: the inverse transform method, the acceptance-rejection method, the transformation methods.
  • Monte Carlo integration methods.
  • Variance Reduction, the importance sampling (sampling importance resampling) and the stratified sampling.
  • Monte Carlo methods in Inference in a Bayesian and frequentist framework.
  • Bootstrap and Jackknife.
  • Permutation Tests for Equal Distributions.

Suggested readings and bibliography

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1. Probability: • Baldi, P. (2011). Calcolo della probabilità. McGraw-Hill; • Grimmett, G. and Welsh, D. (2014). Probability: an introduction. Oxford University Press.

2. Statistics: • Azzalini, A. (1996). Statistical inference based on the likelihood function. Chapmal and Hall/CRC; • Casella, G. and Berger, R. (2001). Statistical inference. Cengage Learning Press.

3. Simulation:

  • Rizzo, M.L. (2015) "Statistical Computing with R  (Second Edtion)" -- Chapman & Hall/CRC The R Series.
  • Ross. S.M. (2006) "Simulation 4th edition" -- Academic Press.
  • Jones, O., Maillardet, R. and Robinson A. (2009). "Introduction to scientific programming and simulation usig R" -- Chapman and Hall/CRC;


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Class schedule

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Last update: 14/02/2017 16:10
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