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

Stuart A. Klugman

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 143

Veröffentlichungsjahr: 2019

Beschreibung

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.

Leseprobe

CONTENTS

Cover

Series Page

Title Page

Copyright

Chapter 1: Introduction

Chapter 2: Solutions

Section 2.2

Chapter 3: Solutions

Section 3.1

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Chapter 4: Solutions

Section 4.2

Chapter 5: Solutions

Section 5.2

Section 5.3

Section 5.4

Chapter 6: Solutions

Section 6.1

Section 6.5

Section 6.6

Chapter 7: Solutions

Section 7.1

Section 7.2

Section 7.3

Section 7.5

Chapter 8: Solutions

Section 8.2

Section 8.3

Section 8.4

Section 8.5

Section 8.6

Chapter 9: Solutions

Section 9.1

Section 9.2

Section 9.3

Section 9.4

Section 9.6

Section 9.7

Section 9.8

Chapter 10: Solutions

Section 10.2

Section 10.3

Section 10.4

Section 10.5

Chapter 11: Solutions

Section 11.2

Section 11.3

Section 11.4

Section 11.5

Section 11.6

Section 11.7

Chapter 12: Solutions

Section 12.7

Chapter 13: Solutions

Section 13.2

Section 13.3

Chapter 14: Solutions

Section 14.2

Section 14.3

Section 14.4

Section 14.5

Section 14.6

Section 14.7

Section 14.8

Chapter 15: Solutions

Section 15.3

Section 15.4

Section 15.5

Chapter 16: Solutions

Section 16.7

Chapter 17: Solutions

Section 17.9

Chapter 18: Solutions

Section 18.5

Chapter 19: Solutions

Section 19.1

Section 19.2

Section 19.3

Section 19.4

End User License Agreement

List of Tables

Table 9.1

Table 9.2

Table 9.3

Table 9.4

Table 9.5

Table 9.6

Table 11.1

Table 11.2

Table 14.1

Table 14.2

Table 14.3

Table 14.4

Table 14.5

Table 14.6

Table 14.7

Table 14.8

Table 14.9

Table 14.10

Table 15.1

Table 15.2

Table 15.3

Table 15.4

Table 15.5

Table 15.6

Table 15.7

Table 15.8

Table 15.9

Table 15.10

Table 15.11

Table 15.12

Table 15.13

Table 15.14

Table 17.1

Table 17.2

Table 17.3

Table 17.4

Table 17.5

Table 17.6

Table 17.7

Table 17.8

Table 17.9

Table 18.1

Table 18.2

List of Illustrations

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 3.1

Figure 5.1

Figure 14.1

Figure 14.2

Figure 14.3

Figure 14.4

Figure 14.5

Figure 14.6

Figure 15.1

Figure 15.2

Figure 15.3

Figure 15.4

Figure 15.5

Figure 15.6

Figure 15.7

Guide

Cover

Table of Contents

Chapter 1

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Student Solutions Manual to Accompany LOSS MODELS

From Data To Decisions

Fifth Edition

Stuart A. Klugman

Society of Actuaries

Harry H. Panjer

University of Waterloo

Gordon E. Willmot

University of Waterloo

This edition first published 2019

© 2019 John Wiley and Sons, Inc.

Edition History

Wiley (1e, 1998; 2e, 2004; 3e, 2008; and 4e, 2012)

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Library of Congress Cataloging-in-Publication Data

Names: Klugman, Stuart A., 1949- author. | Panjer, Harry H., author. | Willmot, Gordon E., 1957- author.

Title: Loss models : from data to decisions / Stuart A. Klugman, Society of Actuaries, Harry H. Panjer, University of Waterloo, Gordon E. Willmot, University of Waterloo.

Description: 5th edition. | Hoboken, NJ : John Wiley and Sons, Inc., [2018] |

Series: Wiley series in probability and statistics | Includes bibliographical references and index. |

Identifiers: LCCN 2018031122 (print) | ISBN 9781119523789 (hardcover) | ISBN 9781119538059 (solutions manual)

Subjects: LCSH: Insurance–Statistical methods. | Insurance–Mathematical models.

Classification: LCC HG8781 (ebook) | LCC HG8781 .K583 2018 (print) | DDC 368/.01–dc23

LC record available at https://lccn.loc.gov/2018031122

Cover design by Wiley

Chapter 1Introduction

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 2Solutions

Section 2.2

2.1

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.

2.3

. Setting the derivative equal to zero and multiplying by

gives the equation

. This is equivalent to

. The only positive solution is the mode of

.

Figure 2.1 The distribution function for Model 3.

Figure 2.2 The distribution function for Model 4.

Figure 2.3 The distribution function for Model 5.

Figure 2.4 The probability function for Model 3.

Figure 2.5 The density function for Model 4.

Figure 2.6 The density function for Model 5.

Chapter 3Solutions

Section 3.1

3.1

3.2 For Model 1,

,

.

, and

,

.

,

.

For Model 2, , and . and are both infinite, so the skewness and kurtosis are not defined.

For Model 3, and . , , , , , .

For Model 4, and . , , . , , .

For Model 5, and . , , . , , .

3.3 The standard deviation is the mean times the coefficient of variation, or 4, and so the variance is 16. From (3.3), the second raw moment is

. The third central moment is (using Exercise 3.1)

. The skewness is the third central moment divided by the cube of the standard deviation, or

.

3.4 For a gamma distribution, the mean is

. The second raw moment is

, and so the variance is

. The coefficient of variation is

. Therefore

. The third raw moment is

. From Exercise 3.1, the third central moment is

and the skewness is

.

3.5 For Model 1,

For Model 2,

For Model 3,

For Model 4,

The functions are straight lines for Models 1, 2, and 4. Model 1 has negative slope, Model 2 has positive slope, and Model 4 is horizontal.

3.6 For a uniform distribution on the interval from 0 to

w

, the density function is

. The mean residual life is

The equation becomes

with a solution of .

3.7 From the definition,

3.8

3.9 For Model 1, from (3.8),

and from (3.10),

From (3.9),

For Model 2, from (3.8),

and from (3.10),

From (3.9),

For Model 3, from (3.8),

and from (3.10),

For Model 4, from (3.8),

and from (3.10),

3.10 For a discrete distribution (which all empirical distributions are), the mean residual life function is

When d is equal to a possible value of X