Loss Models: From Data to Decisions, 5e Student Solutions Manual
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Loss Models: From Data to Decisions, 5e Student Solutions Manual

Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot

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eBook - ePub

Loss Models: From Data to Decisions, 5e Student Solutions Manual

Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot

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About This Book

Solutions manual to accompany a text with comprehensive coverage of actuarial modeling techniques The Student Solutions Manual to Accompany Loss Models: From Data to Decisions covers solutions related to the companion text. The manual and text are designed for use by actuaries and those studying for the profession. Readers can learn modeling techniques used across actuarial science. Knowledge of the techniques is also beneficial for those who use loss data to build models for risk assessment.

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Information

Publisher
Wiley
Year
2019
ISBN
9781119538066

Chapter 1
Introduction

The solutions presented in this manual reflect the authors' best attempt to provide insights and answers. While we have done our best to be complete and accurate, errors may occur and there may be more elegant solutions. Errata will be linked from the syllabus document for any Society of Actuaries examination that uses this text.
Should you find errors, or if you would like to provide improved solutions, please send your comments to Stuart Klugman at [email protected].

Chapter 2
Solutions

Section 2.2

  1. 2.1
    img
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  2. 2.2 The requested plots follow. The triangular spike at zero in the density function for Model 4 indicates the 0.7 of discrete probability at zero.
  3. 2.3
    img
    . Setting the derivative equal to zero and multiplying by
    img
    gives the equation
    img
    . This is equivalent to
    img
    . The only positive solution is the mode of
    img
    .
    A graphical representation for the distribution function for Model 3, where F(x) is plotted on the y-axis on a scale of 0–1 and x on the x-axis on a scale of 0–5.
    Figure 2.1 The distribution function for Model 3.
    A graphical representation for the distribution function for Model 4, where F(x) is plotted on the y-axis on a scale of 0–1 and x on the x-axis on a scale of 0–500000.
    Figure 2.2 The distribution function for Model 4.
    A graphical representation for the distribution function for Model 5, where F(x) is plotted on the y-axis on a scale of 0–1 and x on the x-axis on a scale of 0–70.
    Figure 2.3 The distribution function for Model 5.
    A graphical representation for the probability function for Model 3, where p(x) is plotted on the y-axis on a scale of 0.1–0.5 and x on the x-axis on a scale of 0–4.
    Figure 2.4 The probability function for Model 3.
    A graphical representation for the density function for Model 4, where f(x) is plotted on the y-axis on a scale of 0–5e-06 and x on the x-axis on a scale of 0–500000.
    Figure 2.5 The density function for Model 4.
    A graphical representation for the density function for Model 5, where f(x) is plotted on the y-axis on a scale of 0–0.025 and x on the x-axis on a scale of 0–70.

Table of contents