Statistical Inference in Financial and Insurance Mathematics with R

Statistical Inference in Financial and Insurance Mathematics with R

1st Edition - November 22, 2017

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  • Author: Alexandre Brouste
  • Hardcover ISBN: 9781785480836
  • eBook ISBN: 9780081012611

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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.

Key Features

  • 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 financial and insurance mathematics
  • Provides the proper description of such statistical experiments and invites readers to seek optimal estimators (performed in R) for such statistical experiments

Readership

Masters students, PHD students in the field of mathematics, finance and economics/insurance; Finance and Insurance company practitioners

Table of Contents

  • Part 1. Inference in Parametric Statistical Experiments
    1. Statistical Experiments
    2. Statistical Inference
    3. Asymptotic Efficiency

    Part 2. Statistical Inference for Insurance
    4. Statistical Experiments in Insurance

    Part 3. Statistical Inference for Finance
    5. Homogeneous Diffusion Processes
    6. Statistical Experiments in Finance

Product details

  • No. of pages: 202
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2017
  • Published: November 22, 2017
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785480836
  • eBook ISBN: 9780081012611

About the Author

Alexandre Brouste

Alexandre Brouste is a Professor in Statistics with the Institute of Risk and Insurance at Le Mans University, France

Affiliations and Expertise

Le Mans University, France

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