Statistical Inference in Financial and Insurance Mathematics with R Optimization in Insurance and Finance Set 1st Edition by Alexandre Brouste 0081012611 9780081012611

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ISBN-10 :  0081012611 

ISBN-13 :  9780081012611

Author :  Alexandre Brouste 

Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consisting of probability measures of an exponential type. However, the aforementioned applications also offer non-classical experiments implying observation samples of independent but not identically distributed random variables or even dependent random variables.

Three examples of such experiments are treated in this book. First, the Generalized Linear Models are studied. They extend the standard regression model to non-Gaussian distributions. Statistical experiments with Markov chains are considered next. Finally, various statistical experiments generated by fractional Gaussian noise are also described.

Statistical Inference in Financial and Insurance Mathematics with R (Optimization in Insurance and Finance Set) 1st Table of contents:

Part 1: Inference in Parametric Statistical Experiments
1: Statistical Experiments
Abstract
1.1 Dominated and homogeneous statistical experiments
1.2 Experiments generated by a sample of independent and identically distributed random variables
1.3 Probability measures of exponential type
2: Statistical Inference
Abstract
2.1 Asymptotic properties of sequences of estimators
2.2 Examples of sequences of estimators
2.3 Asymptotic normality
3: Asymptotic Efficiency
Abstract
3.1 Likelihood ratio, local asymptotic properties of the likelihoods and the van Trees inequality
3.2 LAN property for different statistical experiments
3.3 Asymptotic efficiency of some sequence of estimators
Part 2: Statistical Inference for Insurance
4: Statistical Experiments in Insurance
Abstract
4.1 Statistical inference in generalized linear models
4.2 Score and Fisher information of GLM statistical experiments
4.3 Asymptotic properties of the sequence of maximum likelihood estimators
4.4 Numerical approximations of the sequence of maximum likelihood estimators
Part 3: Statistical Inference for Finance
5: Homogeneous Diffusion Processes
Abstract
5.1 Examples of pricing in finance
5.2 Examples of closed-form transition probability density functions
5.3 Simulation of diffusions
5.4 General classes of diffusion processes
6: Statistical Experiments in Finance
Abstract
6.1 Large-sample convergence scheme
6.2 Mixed convergence scheme
6.3 High-frequency convergence scheme
Appendix 1: Cholesky Method
Appendix 2: L2(ν)-Differentiable Family of Probability Measures
A2.1 Differentiability in quadratic mean
A2.2 More regular models
A2.3 Classical examples

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