Contributions to the Economics of Index Based Insurance Schemes (eBook)

Dr. Matthias Rödl wrote his dissertation under the supervision of Prof. Dr. Peter-J. Jost at the chair of organization theory at WHU - Otto Beisheim School of Management, Vallendar. He picked up the idea for his dissertation during his time as a microfinance expert in India. Nowadays he lives in Germany working as a finance professional.

Foreword 6
Preface 7
Contents 9
List of Figures 12
List of Symbols 13
1 Introduction 15
1.1 General approach 17
1.2 State of research 17
1.3 Organisation of the thesis 19
2 Demand 20
2.1 Introduction 20
2.2 The model 26
2.3 Necessities and utility comparison 31
2.4 Optimal demand 39
2.5 Correlation and demand 45
2.6 Risk aversion 54
2.7 Comparative statistics and background risks 65
2.8 Idiosyncratic risk, common shock, and insurance 74
2.9 Conclusions 82
3 Supply 85
3.1 Introduction 85
3.2 The classic insurance 86
3.3 The index based insurance approach 90
3.4 The insurer’s profit under an index based insurance 95
3.5 Observation costs 102
3.6 Conclusions and critical reflection 108
4 Self-insurance 113
4.1 Introduction – Index insurance demand, self-insurance, and self-protection 113
4.2 Model 114
4.3 Successive decisions 116
4.4 Simultaneous decisions 125
4.5 Self-insurance and correlation 129
4.6 Conclusions 138
5 Moral hazard and group sample observation 143
5.1 Introduction 143
5.2 The model 144
5.3 Separate observation 147
5.4 Group sample observation 152
5.4.1 Perfect dependence 153
5.4.2 Independence 162
5.4.3 Mere dependence 163
5.5 Conclusions 168
5.6 Reflection and outlook 171
6 Conclusions and outlook 173
Appendix 176
A.1 Chapter Demand 176
A.1.1 Proof of Proposition 2 176
A.1.2 Arrow-Pratt measurement of risk aversion 178
A.1.3 Risk aversion: Second example 179
A.1.4 Proof of Proposition 11 Part (b): Index insurance and pooling insurance separately 180
A.1.5 Proof of Proposition 11 Part (b): Combination of both insurance schemes 180
A.1.6 Proof of Proposition 11 Part (b): Maximum 183
A.1.7 Proof of Proposition 11 Part (c): Basic chance remains 186
A.1.8 Proof of Proposition 11 Part (c): Maximum 190
A.2 Chapter Supply 193
A.2.1 Proof of Lemma 12 193
A.2.2 Profit subject to a chance in loss probability 195
A.2.3 Alternative proof of Lemma 13 196
A.2.4 Proof of Lemma 13 (b) 196
A.2.5 Proof of Proposition 16 204
A.2.6 Proof of Proposition 17 Part (a) 213
A.2.7 Calculation for Proposition 17 Part (b) 219
A.2.8 Calculation for Proposition 18 Part (d) 219
A.2.9 Calculation for Proposition 18 Part (e) 221
A.2.10 Proof of Proposition 18 Part (g) 222
A.3 Chapter Effort 225
A.3.1 Auxiliary calculation for Corollary 20 225
A.3.2 Auxiliary calculation for Proposition 22 226
A.3.3 Proof of Proposition 23 226
A.3.4 Proof of Proposition 24 239
A.3.5 Calculations for Lemma 25 245
A.4 Moral hazard and group sample observation 246
A.4.1 Separate observation: Deflection 246
A.4.2 Explanations for Section 5.4.1 Perfect dependence 247
A.4.3 Three-insured 248
A.4.4 Proof of Proposition 28 251
A.4.5 Ex-ante observation with ex-post announcement 255
A.4.6 Random selection 256
A.4.7 Always selecting randomly 257
A.4.8 Calculation for Section 5.4.3 Mere dependence 259
References 260