Statistical Inference in Financial and Insurance Mathematics with R

Author： Brouste   Alexandre  

Publisher： Elsevier Science‎

Publication year： 2017

E-ISBN: 9780081012611

P-ISBN(Paperback): 9781785480836

Subject： F830 Financial, banking theory

Keyword： 概率论（几率论、或然率论）,财政、金融

Language： ENG

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Description

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.

In this book, asymptotic properties of several sequences of estimators are detailed. The notion of asymptotical efficiency is discussed for the different statistical experiments considered in order to give the proper sense of estimation risk. Eighty examples and computations with R software are given throughout the text.

  • Examines a range of statistical inference methods in the context of finance and insurance applications
  • Presents the LAN (local asymptotic normality) property of likelihoods
  • Combines the proofs of LAN property for different statistical experiments that appears in financi

Chapter

Front Cover

Dedication

Statistical Inference in Financial and Insurance Mathematics with R

Copyright

Contents

Preface

List of Notations

Introduction

Part 1: Inference in Parametric Statistical Experiments

1. Statistical Experiments

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

2.1. Asymptotic properties of sequences of estimators

2.2. Examples of sequences of estimators

2.3. Asymptotic normality

3. Asymptotic Efficiency

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

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

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

6.1. Large-sample convergence scheme

6.2. Mixed convergence scheme

6.3. High-frequency convergence scheme

Appendices

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

Appendix 3: Stochastic Calculus

Itô’s integral and Itô’s formula

Itô’s formula for diffusion processes

Bibliography

Index

Back Cover

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