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OPTIMAL INCENTIVE-COMPATIBLE INSURANCE WITH BACKGROUND RISK

Published online by Cambridge University Press:  29 March 2021

Yichun Chi  and
Ken Seng Tan
Yichun Chi*
Affiliation:
China Institute for Actuarial Science Central University of Finance and Economics, Beijing102206, China E-Mail: [email protected]
Ken Seng Tan
Affiliation:
Division of Banking & Finance, Nanyang Business School Nanyang Technological University, Singapore E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

Keywords

Background riskconditional expectation functionincentive compatibilitymean-variance preferenceoptimal insurance designD81G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 661 - 688
Copyright
© 2021 by Astin Bulletin. All rights reserved

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References

Arrow, K.J. (1963) Uncertainty and the welfare economics of medical care. American Economic Review, 53(5), 941–973.Google Scholar
Borch, K. (1960) An attempt to determine the optimum amount of stop loss reinsurance. In Transactions of the 16th International Congress of Actuaries, Vol. I, pp. 597–610.Google Scholar
Cai, J. and Wei, W. (2012) Optimal reinsurance with positively dependent risks. Insurance: Mathematics and Economics, 50(1), 57–63.Google Scholar
Cheung, K.C. (2010) Optimal reinsurance revisited—A geometric approach. ASTIN Bulletin, 40(1), 221–239.CrossRefGoogle Scholar
Chi, Y. (2012) Reinsurance arrangements minimizing the risk-adjusted value of an insurer’s liability. ASTIN Bulletin, 42(2), 529–557.Google 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 Wei, W. (2018). Optimum insurance contracts with background risk and higher-order risk attitudes. ASTIN Bulletin, 48(3), 1025–1047.CrossRefGoogle Scholar
Chi, Y. and Wei, W. (2020) Optimal insurance with background risk: An analysis of general dependence structures. Finance and Stochastics, 24(4), 903–937.CrossRefGoogle Scholar
Dana, R.A. and Scarsini, M. (2007) Optimal risk sharing with background risk. Journal of Economic Theory, 133, 152–176.CrossRefGoogle Scholar
Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D. (2002) The concept of comonotonicity in actuarial science and finance: Theory. Insurance: Mathematics and Economics, 31(1), 3–33.Google Scholar
Doherty, N.A. and Schlesinger, H. (1983) The optimal deductible for an insurance policy when initial wealth is random. Journal of Business, 56(4), 555–565.CrossRefGoogle Scholar
Eeckhoudt, L. and Kimball, M. (1992) Background risk, prudence, and the demand for insurance. In Contributions to Insurance Economics, (ed. Dionne, G. ), pp. 239–254. Springer.CrossRefGoogle Scholar
Franke, G., Schlesinger, H. and Stapleton, R.C. (2011) Risk taking with additive and multiplicative background risks. Journal of Economic Theory, 146(4), 1547–1568.CrossRefGoogle Scholar
Gollier, C. (1996) Optimum insurance of approximate losses. The Journal of Risk and Insurance, 63(3), 369–380.CrossRefGoogle Scholar
Graf, J.M. and Schulenburg, V.D. (1986) Optimal insurance purchasing in the presence of compulsory insurance and uninsurable risks. The Geneva Papers on Risk and Insurance, 38, 5–16.Google Scholar
Hong, S.K., Lew, K.O., MacMinn, R. and Brockett, P. (2011) Mossin’s theorem given random initial wealth. The Journal of Risk and Insurance, 78(2), 309–324.CrossRefGoogle Scholar
Huang, H.H., Shiu, Y.M. and Wang, C.P. (2013) Optimal insurance contract with stochastic background wealth. Scandinavian Actuarial Journal, 2, 119–139.CrossRefGoogle Scholar
Huberman, G., Mayers, D. and Smith, C.W. Jr. (1983) Optimal insurance policy indemnity schedules. The Bell Journal of Ecoonomics, 14(2), 415–426.CrossRefGoogle Scholar
Kaluszka, M. (2001) Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics and Economics, 28(1), 61–67.Google Scholar
Lu, Z.Y., Liu, L.P., Zhang, J.Y. and Meng, L.L. (2012) Optimal insurance under multiple sources of risk with positive dependence. Insurance: Mathematics and Economics, 51(2), 462–471.Google Scholar
Lu, Z.Y., Meng, S.W., Liu, L.P. and Han, Z. (2018) Optimal insurance design under background risk with dependence. Insurance: Mathematics and Economics, 80, 15–28.Google Scholar
Mahul, O. (2000) Optimal insurance design with random initial wealth. Economics Letters, 69(3), 353–358.CrossRefGoogle Scholar
Markowitz, H. (1952) Portfolio selection. The Journal of Finance, 7(1), 77–91.Google Scholar
Marlin, P. (1984) Fitting the log-normal distribution to loss data subject to multiple deductibles. The Journal of Risk and Insurance, 51(4), 687–701.CrossRefGoogle Scholar
Mayers, D. and Smith, C.W. Jr. (1983) The interdependence of individual portfolio decisions and the demand for insurance. Journal of Political Economy, 91(2), 304–311.CrossRefGoogle Scholar
Mossin, J. (1968) Aspects of rational insurance purchasing. Journal of Political Economy, 76(4), 553–568.Google Scholar
Ohlin, J. (1969) On a class of measures of dispersion with application to optimal reinsurance. ASTIN Bulletin, 5(2), 249–266.CrossRefGoogle Scholar
Raviv, A. (1979) The design of an optimal insurance policy. American Economic Review, 69(1), 84–96.Google Scholar
Vercammen, J. (2001) Optimal insurance with nonseparable background risk. The Journal of Risk and Insurance, 68(3), 437–448.CrossRefGoogle Scholar