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OPTIMAL REINSURANCE DESIGN WITH DISTORTION RISK MEASURES AND ASYMMETRIC INFORMATION

Published online by Cambridge University Press:  29 March 2021

Tim J. Boonen Open the ORCID record for Tim J. Boonen [Opens in a new window]  and
Yiying Zhang Open the ORCID record for Yiying Zhang [Opens in a new window]
Tim J. Boonen
Affiliation:
Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands, E-Mail: [email protected]
Yiying Zhang*
Affiliation:
School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin300071, P.R. China, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

Keywords

Optimal reinsuranceasymmetric informationindividual rationalityincentive compatibilitydistortion risk measureC61G22G32
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 607 - 629
Copyright
© 2021 by Astin Bulletin. All rights reserved

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References

Akerlof, G.A. (1970) The market for “lemons”: Qualitative uncertainty and the market mechanism. Quarterly Journal of Economics, 84, 488–500.CrossRefGoogle Scholar
Amarante, M., Ghossoub, M. and Phelps, E. (2015) Ambiguity on the insurer’s side: The demand for insurance. Journal of Mathematical Economics, 58, 61–78.CrossRefGoogle Scholar
Anthropelos, M. and Boonen, T.J. (2020) Nash equilibria in optimal reinsurance bargaining. Insurance: Mathematics and Economics, 93, 196–205.Google Scholar
Assa, H. (2015) On optimal reinsurance policy with distortion risk measures and premiums. Insurance: Mathematics and Economics, 61, 70–75.Google Scholar
Barrieu, P. and El Karoui, N. (2005) Inf-convolution of risk measures and optimal risk transfer. Finance and Stochastics, 9, 269–298.CrossRefGoogle Scholar
Boonen, T.J., Cheung, K.C. and Zhang, Y. (2021) Bowley reinsurance with asymmetric information on the insurer’s risk preferences. Scandinavian Actuarial Journal, forthcoming, https://doi.org/10.1080/03461238.2020.1867631.CrossRefGoogle Scholar
Boonen, T.J., Tan, K.S. and Zhuang, S.C. (2018) Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability. mimeo, available at SSRN: https://ssrn.com/abstract=3143224.CrossRefGoogle Scholar
Carlier, G. and Dana, R.-A. (2003) Pareto efficient insurance contracts when the insurer’s cost function is discontinuous. Economic Theory, 21, 871–893.CrossRefGoogle Scholar
Chade, H. and Schlee, E. (2012) Optimal insurance with adverse selection. Theoretical Economics, 7, 571–607.CrossRefGoogle Scholar
Cheung, K.C., Dhaene, J., Lo, A. and Tang, Q. (2014) Reducing risk by merging counter-monotonic risks. Insurance: Mathematics and Economics, 54, 58–65.Google Scholar
Cheung, K.C. and Lo, A. (2017) Characterizations of optimal reinsurance treaties: A cost-benefit approach. Scandinavian Actuarial Journal, 2017, 1–28.CrossRefGoogle Scholar
Cheung, K.C., Yam, S.C.P., Yuen, F.L. and Zhang, Y. (2020) Concave distortion risk minimizing reinsurance design under adverse selection. Insurance: Mathematics and Economics, 91, 155–165.Google Scholar
Chi, Y. (2012) Reinsurance arrangements minimizing the risk-adjusted value of an insurer’s liability. ASTIN Bulletin, 42, 529–557.Google Scholar
Cui, W., Yang, J. and Wu, L. (2013) Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles. Insurance: Mathematics and Economics, 53, 74–85.Google Scholar
De Giorgi, E. and Post, T. (2008) Second-order stochastic dominance, reward-risk portfolio selection, and the CAPM. Journal of Financial and Quantitative Analysis, 43, 525–546.CrossRefGoogle Scholar
Denuit, M. and Vermandele, C. (1998) Optimal reinsurance and stop-loss order. Insurance: Mathematics and Economics, 22, 229–233.Google Scholar
Geruso, M. (2017) Demand heterogeneity in insurance markets: Implications for equity and efficiency. Quantitative Economics, 8, 929–975.CrossRefGoogle Scholar
Huberman, G., Mayers, D. and Smith, C.W. Jr. (1983) Optimal insurance policy indemnity schedules. Bell Journal of Economics, 14, 415–426.CrossRefGoogle Scholar
Julien, B. (2000) Participation Constraints in adverse selection models. Journal of Economic Theory, 93, 1–47.CrossRefGoogle Scholar
Laffont, J.J. and Martimort, D. (2009) The Theory of Incentives: The Principal-Agent Model. New Jersey, USA: Princeton University Press.CrossRefGoogle Scholar
Landsberger, M. and Meilijson, I. (1994) Monopoly insurance under adverse selection when agents differ in risk aversion. Journal of Economic Theory, 63, 392–407.CrossRefGoogle Scholar
Landsberger, M. and Meilijson, I. (1999) A general model of insurance under adverse selection. Economic Theory, 14, 331–352.CrossRefGoogle Scholar
Lo, A., Tang, Q. and Tang, Z. (2021) Universally marketable insurance under multivariate mixtures. ASTIN Bulletin, 51, 221–243.Google Scholar
Raviv, A. (1979) The design of an optimal insurance policy. American Economic Review, 69, 84–96.Google Scholar
Rothschild, M. and Stiglitz, J. (1976) Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. Quarterly Journal of Economics, 90, 629–649.CrossRefGoogle Scholar
Schmeidler, D. (1986) Integral representation without additivity. Proceedings of the American Mathematical Society, 97, 255–261.CrossRefGoogle Scholar
Wang, S.S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin, 26, 71–92.CrossRefGoogle Scholar
Wang, S.S., Young, V.R. and Panjer, H.H. (1997) Axiomatic characterization of insurance prices. Insurance: Mathematics and Economics, 21, 173–183.Google Scholar
Yaari, M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95–115.CrossRefGoogle Scholar
Young, V.R. and Browne, M.J. (2000) Equilibrium in competitive insurance markets under adverse selection and Yaari’s dual theory of risk. Geneva Papers on Risk and Insurance Theory, 25, 141–157.CrossRefGoogle Scholar
Zhuang, S.C., Weng, C., Tan, K.S. and Assa, H. (2016) Marginal indemnification function formulation for optimal reinsurance. Insurance: Mathematics and Economics, 67, 65–76.Google Scholar
Zhuang, S.C., Boonen, T.J., Tan, K.S. and Xu, Z.Q. (2017) Optimal insurance in the presence of reinsurance. Scandinavian Actuarial Journal, 2017, 535–554.CrossRefGoogle Scholar