Modelos de Risco (1 º Sem 2017/2018)

  1. CONSTRUCTION OF EMPIRICAL MODELS

   1.1.    Review of basic statistical concepts

            1.1.1. Introduction. Sampling and sampling distribution

            1.1.2. Point estimation with emphasis on measures of quality

            1.1.3. Interval estimation

            1.1.4. Tests of hypothesis

   1.2.   Estimation for complete data

           1.2.1. The empirical distribution for complete individual data

           1.2.2. The empirical distribution for grouped data

   1.3.  Estimation for modified data

           1.3.1. Means, variance and interval estimation

           1.3.2. Kernel density models

           1.3.3. Approximations for large data sets

2. PARAMETRIC STATISTICAL METHODS

    2.1.  Frequentist estimation

           2.1.1. Methods of moments and percentile matching

           2.1.2. Maximum likelihood estimation (individual, grouped, censored and truncated data)

           2.1.3. Variance and interval estimation

           2.1.4. Non-normal confidence intervals

    2.2. Bayesian Estimation

           2.2.1 Definitions and Bayes' theorem

           2.2.2 Inference and prediction

           2.2.3 Conjugate prior distributions

    2.3. Model selection

           2.3.1. Introduction

           2.3.2. Representation of the data and model

           2.3.3. Graphical comparison of the density and distribution functions

           2.3.4. Hypothesis tests

           2.3.5. Selecting a model

3. SIMULATION AND BOOTSTRAP

   3.1. Simulation

          3.1.1. Basics of simulation

          3.1.2. Examples of simulation in actuarial modeling and finance

   3.2. Bootstrap

          3.2.1. Introduction to bootstrapping

          3.2.2. Bootstrap distributions and standards errors

          3.2.3. Bootstrap confidence intervals

          3.2.4. Significance testing using permutation tests