Quantitative Finance and Insurance

Numerical and Statistical Methods for Finance

Numerical and Statistical Methods for Finance

Academic year 2013/2014

Sommario del corso

• Course objectives
• Results of learning outcomes
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

Ability to solve, through the use of simulation tools, some standard problems in mathematical analysis and statistics. Ability to apply statistical concepts and statistical techniques with respect to the point estimation, hyphotesis testing and confidence sets.

Results of learning outcomes

The acquired skills give students the opportunity of understanding some of the probabilistic tools for simulation and the methodology of statistical inference based on likelihood functions.

Program

1. Advances statistical inference

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

The module provides an introduction to simulation using the software R. During the course the emphasis will be given to the problem of generating discrete and continuous random variables. Topics include
• Functions of random variables (univariate and multivariate, discrete and continuous) and their application in generating random numbers.
• Random numbers: pseudorandom number generation; using random number to evaluate integrals.
• Generating discrete random variables: the inverse transform method; generating a Poisson random variable; generating Binomial random variables; the acceptance-rejection technique; generating random vector.
• Generating continuous random variables: the inverse transform algorithm; the rejection method; the polar method for generating normal random variables; generating an homogeneous and nonhomogeneous Poisson process.

Ross. S.M. (2002) Simulation. Academic Press.

Jones, O., Maillardet, R. and Robinson A. (2009) Introduction to scientific programming and simulation usig R. Chapman and Hall/CRC

Azzalini, A. (1996) Statistical inference based on the likelihood function. Chapmal and Hall/CRC.

Note

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums