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INDEX INSURANCE DESIGN

Published online by Cambridge University Press:  27 March 2019

Jinggong Zhang ,
Ken Seng Tan  and
Chengguo Weng
Jinggong Zhang
Affiliation:
Division of Banking and FinanceNanyang Technological University50 Nanyang Ave 639798, Singapore E-Mail: jgzhang@ntu.edu.sg
Ken Seng Tan
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of WaterlooM3-200 University Avenue West, Waterloo Ontario N2L 3G1, Canada E-Mail: kstan@uwaterloo.ca
Chengguo Weng*
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of WaterlooM3-200 University Avenue West, Waterloo Ontario N2L 3G1, Canada E-Mail: c2weng@uwaterloo.ca
*
E-Mail: c2weng@uwaterloo.ca
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Abstract

In this article, we study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract and develop an effective numerical procedure to derive the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly nonlinear and even non-monotonic function of the index variable in order to align with the actual loss variable so as to achieve the best reduction in basis risk. Due to the generality of model setup, our proposed method is readily applicable to a variety of insurance applications including index-linked mortality securities, weather index agriculture insurance, and index-based catastrophe insurance. Our method is illustrated by numerical examples where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of basis risk reduction.

Keywords

Index insurancebasis riskutility maximizationinsurance subsidiaryODE method
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 491 - 523
Copyright
Copyright © Astin Bulletin 2019 

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