A Mathematical Technique of Computing Technical Provisions and Premiums in General Business Insurance Under the Influence of Chain-Ladder and Cape Cod Framework

ABSTRACT

An insurance company promises its policyholders to pay out benefits if certain events occur, for example, events such as a car accident and health conditions. When this is happens, the insurance company has a liability to pay the claims by technical provisions or claim reserving. The calculation of claim reserving must be done carefully in such a way that it should not cause loss to the company. Two of the common methods to calculate technical provisions in non-life insurance are the chain ladder method (CL) and Cape Cod method (CC). The Chain-Ladder method (CL) uses an algorithm that can be used to estimate claim reserving in the future. The Chain-Ladder method (CL) estimates the claim reserving to be paid by using run-off triangle data. The rows on a run-off triangle data represent claim occurrence periods and the columns represent development periods, the periods when claim were settled. The real data used is a claim amount observed in the past that is located in the upper-left triangle, and the lower triangle has to be estimated. The Cape Cod method (CC) was developed to overcome the shortcomings of the Chain-Ladder (CL) method by introducing lag factors and information about the earned premium. The basic idea of Cape Cod method is to compare known losses with used-up premiums. The Cape Cod method (CC) instead of requiring a priori loss ratio, it estimates one with help of a measure of exposure and claims to date. The purpose of this research is to show basic calculation for technical provisions and premiums in non-life insurance. One of the objectives is to construct practical examples and calculated premiums. The main goal is to get familiar with different products in non-life insurance and to see how important certain classes of products are by considering the amount of paid premiums and made provisions. Building upon existing theory we then present and use mathematical equations and methods used for the calculations of premiums and claim provision.

 

TABLE OF CONTENTS

Cover Page      -           -           -           -           -           -           -           -           -           -           i

Title Page-       -           -           -           -           -           -           -           -           -           -           ii

Declaration      -           -           -           -           -           -           -           -           -           -           iii

Approval page -          -           -           -           -           -           -           -           -           -           iv

Dedication      -           -           -           -           -           -           -           -           -           -           v

Acknowledgment       -           -           -           -           -           -           -           -           -           vi

Table of Contents       -           -           -           -           -           -           -           -           -           vii

Abstract          -           -           -           -           -           -           -           -           -           -           x

CHAPTER ONE: GENERAL INTRODUCTION

1.1       Background of the Study       -           -           -           -           -           -           -           1

1.2       Statement of the Problem       -           -           -           -           -           -           -           3

1.3       Objectives of the Study          -           -           -           -           -           -           -           4

1.4       Research Questions     -           -           -           -           -           -           -           -           5

1.5       Significance of the Study       -           -           -           -           -           -           -           5

1.6       Scope of the Study     -           -           -           -           -           -           -           -           6

1.7       Definition of Terms    -           -           -           -           -           -           -           -           6

CHAPTER TWO: LITERATURE REVIEW

2.0       Introduction                -           -           -           -           -           -           -           -           8

2.1       Conceptual Review                 -           -           -           -           -           -           -           8

2.1.1    Concept of technical provisions -       -           -           -           -           -           -           8

2.1.2    Reserves in non-life insurance            -           -           -           -           -           -          9

2.1.3    The types of reserves in non-life insurance-    -           -           -           -           -           9

2.1.4    Methods of calculating loss reserves  -           -           -           -           -           -           15

2.2       Theoretical Review                 -           -           -           -           -           -           -           17

2.3       Empirical Review        -           -           -           -           -           -           -           -           23

2.3.1    Empirical perspective of non-life insurance pricing    -           -           -           -           23

2.3.2    Empirical review of relevant literature work  -           -           -           -           -           28

CHAPTER THREE:  METHODOLOGY

3.0       Introduction    -          -           -           -           -           -           -           -           -           32

3.1       Estimation and calculation procedures of the premium and technical

provisions for  insurance claims          -           -           -           -           -           -           32

3.2       Data requirements       -           -           -           -           -           -           -           -           33

3.3       Mathematical model   -           -           -           -           -           -           -           -           34

3.4       Development factors   -           -           -           -           -           -           -           -           37

3.5       Data structure for Cape Cod method -           -           -           -           -           -           46    

3.6       Parameter estimation   -           -           -           -           -           -           -           -           50

3.7       Premium calculation in non-life insurance     -           -          -           -          -           53

3.8       Underwriting risk in non-life insurance company      -          -           -          -           53

3.9        Ruin theory   -          -            -         -            -            -          -           -          -           54

3.10      Premium principles   -            -           -           -           -           -           -           -           56

3.11      Experience rating and credibility premium    -            -          -           -          -          59

3.12      credibility premium    -           -           -           -           -           -           -           -           60

3.13      Deductibles                -           -           -           -           -           -           -           -           64

3.14      Non-life insurance claims provisions -           -            -          -           -          -           66

3.15      Chain-Ladder method -            -         -            -            -          -           -          -        66

3.16       Cape Cod method     -            -          -          -           -          -             -          -          70      


CHAPTER FOUR: DATA PRESENTATION AND ANALYSIS

4.0       Data Analysis  -           -           -           -           -           -           -           -           -           74

4.1       Discussion of Result   -           -           -           -           -           -           -           -          81

4.2       Appendix        -           -           -           -           -           -           -           -           -          86

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION

5.0       Introduction    -           -           -           -           -           -           -           -           -           88

5.1       Summary of Findings -           -           -           -           -           -           -           -           88

5.2        Conclusion     -           -           -           -           -           -           -           -           -           89

5.3       Recommendations      -           -           -           -           -           -           -           -           90

             References     -           -           -           -           -           -           -           -           -           91

                                                     


 

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APA

Omede, D. (2023). A Mathematical Technique of Computing Technical Provisions and Premiums in General Business Insurance Under the Influence of Chain-Ladder and Cape Cod Framework. Afribary. Retrieved from https://afribary.com/works/a-mathematical-technique-of-computing-technical-provisions-and-premiums-in-general-business-insurance-under-the-influence-of-chain-ladder-and-cape-cod-framework

MLA 8th

Omede, David "A Mathematical Technique of Computing Technical Provisions and Premiums in General Business Insurance Under the Influence of Chain-Ladder and Cape Cod Framework" Afribary. Afribary, 02 Nov. 2023, https://afribary.com/works/a-mathematical-technique-of-computing-technical-provisions-and-premiums-in-general-business-insurance-under-the-influence-of-chain-ladder-and-cape-cod-framework. Accessed 14 Jul. 2024.

MLA7

Omede, David . "A Mathematical Technique of Computing Technical Provisions and Premiums in General Business Insurance Under the Influence of Chain-Ladder and Cape Cod Framework". Afribary, Afribary, 02 Nov. 2023. Web. 14 Jul. 2024. < https://afribary.com/works/a-mathematical-technique-of-computing-technical-provisions-and-premiums-in-general-business-insurance-under-the-influence-of-chain-ladder-and-cape-cod-framework >.

Chicago

Omede, David . "A Mathematical Technique of Computing Technical Provisions and Premiums in General Business Insurance Under the Influence of Chain-Ladder and Cape Cod Framework" Afribary (2023). Accessed July 14, 2024. https://afribary.com/works/a-mathematical-technique-of-computing-technical-provisions-and-premiums-in-general-business-insurance-under-the-influence-of-chain-ladder-and-cape-cod-framework

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