Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T13:08:06.399Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arrow, K.J. (1963) Uncertainty and the welfare economics of medical care. American Economic Review, 53(5), 941–973.Google Scholar
Barnett, B. J. andMahul, O. (2007) Weather index insurance for agriculture and rural areas in lower-income countries. American Journal of Agricultural Economics, 89(5), 1241–1247.CrossRefGoogle Scholar
Bokushevaa, B., Koganb, F., Vitkovskayac, I., Conradta, S. and Batyrbayevacaa, M. (2016) Satellite-based vegetation health indices as a criteria for insuring against drought-related yield losses. Agricultural and Forest Meteorology, 220, 200–206.CrossRefGoogle Scholar
Borch, K. (1960) An attempt to determine the optimum amount of stop loss reinsurance. Transactions of the 16th International Congress of Actuaries, I, 597–610.Google Scholar
Burden, R.L. and Faires, J.D. (2011) Numerical Analysis. 9th edition. Brooks/Cole, Boston, USA.Google Scholar
Carter, M.R., Cheng, L. and Sarris, A. (2016) Where and how index insurance can boost the adoption of improved agricultural technologies. Journal of Development Economics, 118, 59–71.CrossRefGoogle Scholar
Carter, M.R., De Janvry, A., Sadoulet, E. and Sarris, A. (2014) Index-based weather insurance for developing countries: A review of evidence and a set of propositions for up-scaling. FERDI Working Paper 112.Google Scholar
Chantarat, S., Barrett, C.B., Mude, A.G. and Turvey, C.G. (2007) Using weather index insurance to improve drought response for famine prevention. American Journal of Agricultural Economics, 89(5), 1262–1268.CrossRefGoogle Scholar
Chantarat, S., Mude, A.G., Barrett, C.B. and Carter, M.R. (2013) Designing indexbased livestock insurance for managing asset risk in northern Kenya. Journal of Risk and Insurance, 80(1), 205–237.CrossRefGoogle Scholar
Chi, Y. and Tan, K.S. (2011) Optimal reinsurance under VaR and CVaR risk measures: A simplified approach. ASTIN Bulletin, 41(2), 487–509.Google Scholar
Chi, Y. and Weng, C. (2013) Optimal reinsurance subject to Vajda condition. Insurance: Mathematics and Economics, 53(1), 179–189.Google Scholar
Conradt, S., Finger, R. and Sporri, M. (2015) Flexible weather index-based insurance design. Climate Risk Management, 10, 106–117.CrossRefGoogle Scholar
Cummins, J.D., Lalonde, D. and Phillips, R.D. (2004) The basis risk of catastrophic-loss index securities. Journal of Financial Economics, 71(1), 77–111.CrossRefGoogle Scholar
Dana, R.A. and Scarsini, M. (2007) Optimal risk sharing with background risk. Journal of Economic Theory, 133(1), 152–176.CrossRefGoogle Scholar
Doherty, N.A. and Schlesinger, H. (1983) Optimal insurance in incomplete markets. Journal of Political Economy, 91(6), 1045–1054.CrossRefGoogle Scholar
Elabeda, G., Bellemareb, M.F., Carter, M.R. and Guirkinger, C. (2013) Managing basis risk with multiscale index insurance. Agricultural Economics, 44, 419–431.CrossRefGoogle Scholar
Giné, X., Townsend, R. and Vickery, J. (2007) Statistical analysis of rainfall insurance payouts in Southern India. American Journal of Agricultural Economics, 89(5), 1248–1254.CrossRefGoogle Scholar
International Fund for Agricultural Development World Food Program (2010) The potential for scale and sustainability in weather index insurance for agriculture and rural livelihoods. Technical Report.Google Scholar
Jensen, N.D., Barrett, C.B. and Mude, A.G. (2016) Index insurance quality and basis risk: Evidence from northern Kenya. American Journal of Agricultural Economics, 98(5), 1450–1469.CrossRefGoogle Scholar
Lin, Y. and Cox, S.H. (2008) Securitization of catastrophe mortality risks. Insurance: Mathematics and Economics, 42(2), 628–637.Google Scholar
Mahul, O. (2000) Optimum crop insurance under joint yield and price risk. Journal of Risk and Insurance, 67(1), 109–122.CrossRefGoogle Scholar
Mahul, O. and Wright, B.D. (2003) Designing optimal crop revenue insurance. American Journal of Agricultural Economics, 85(3), 580–589.CrossRefGoogle Scholar
Miranda, M.J. and Farrin, K.M. (2012) Index insurance for developing countries. Applied Economic Perspectives and Policy, 34(3), 391–427.CrossRefGoogle Scholar
Okhrin, O., Odening, M. and Xu, W. (2013) Systemic weather risk and crop insurance: The case of China. Journal of Risk and Insurance, 80(2), 351–372.CrossRefGoogle Scholar
Raviv, A. (1979) The design of an optimal insurance policy. The American Economic Review, 69(1), 84–96.Google Scholar
Shi, H. and Jiang, Z. (2016) The efficiency of composite weather index insurance in hedging rice yield risk: Evidence from China. Agricultural Economics, 47(3), 319–328.CrossRefGoogle Scholar
Vercammen, J. (2001) Optimal insurance with nonseparable background risk. Journal of Risk and Insurance, 68(3), 437–447.CrossRefGoogle Scholar