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Pareto-Optimal Reinsurance Policies under TrTVaR Risk Measure
School of Mathematics and Statistics, Shandong Normal University, Jinan, China
School of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 1 School of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 2 School of Mathematics and Statistics, Shandong Normal University, Jinan, China
Journal of Financial Risk Management·Volume 10 (2021)·Pages 260–273·Published 2 August 2021·DOI10.4236/jfrm.2021.103015
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Abstract
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by TrTVaR risk measure. We study optimal reinsurance models from the perspectives of both insurers and reinsurers. To reduce ex-post moral hazard, we assume that reinsurance contracts satisfy the principle of indemnity and the incentive-compatible constraint. When the losses of an insurer and a reinsurer are both measured by TrTVaR risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle and TVaR premium principle, respectively.
KeywordsTrTVaR Risk MeasurePareto-Optimal ReinsuranceTVaR Premium PrincipleThe Expected Value Premium Principle
- Arrow, K. J. (1963). Uncertainty and the Welfare Economics of Medical Care. The American Economic Review, 53, 941-973. https://www.jstor.org/stable/1812044?seq=1
- Asimit, A. V., Badescu, A. M., & Verdonck, T. (2013). Optimal Risk Transfer under Quantile-Based Risk Measurers. Insurance Mathematics and Economics, 53, 252-265. https://doi.org/10.1016/j.insmatheco.2013.05.005
- Bernard, C., & Tian, W. (2009). Optimal Reinsurance Arrangements under Tail Risk Measures. The Journal of Risk and Insurance, 76, 709-725. https://doi.org/10.1111/j.1539-6975.2009.01315.x
- Borch, K. (1960). An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance Reinsurance. Transactions of the 16th International Congress of Actuaries, 2, 597-610.
- Cai, J., & Tan, K. S. (2007). Optimal Retention for a Stop-Loss Reinsurance under the VaR and CTE Risk Measures. ASTIN Bulletin, 37, 93-112. https://doi.org/10.1017/S0515036100014756
- Cai, J., Liu, H. Y., & Wang, R. D. (2017). Pareto-Optimal Reinsurance Arrangements under General Model Settings. Insurance Mathematics and Economics, 77, 24-37. https://doi.org/10.1016/j.insmatheco.2017.08.004
- Cai, J., Tan, K. S., Weng, C., & Zhang, Y. (2008). Optimal Reinsurance under VaR and CTE Risk Measures. Insurance Mathematics and Economics, 43, 185-196. https://doi.org/10.1016/j.insmatheco.2008.05.011
- Cheung, K. C. (2010). Optimal Reinsurance Revisited—A Geometric Approach. ASTIN Bulletin, 40, 221-239. https://doi.org/10.2143/AST.40.1.2049226
- Cheung, K. C., Sung, K., Yam, S., & Yung, S. (2014). Optimal Reinsurance under General Law-Invariant Risk Measures. Scandinavian Actuarial Journal, 1, 72-91. https://doi.org/10.1080/03461238.2011.636880
- Chi, Y., & Tan, K. (2013). Optimal Reinsurance with General Premium Principles. Insurance Mathematics and Economics, 52, 180-189. https://doi.org/10.1016/j.insmatheco.2012.12.001
- Chi, Y., & Tan, K. S. (2011). Optimal Reinsurance under VaR and CVaR Risk Measures: A Simplified Approach. ASTIN Bulletin, 41, 487-509.
- Cont, R., Deguest, R., & Scandalo, G. (2010). Robustness and Sensitivity Analysis of Risk Measurement Procedures. Quantitative Finance, 10, 593-606. https://doi.org/10.1080/14697681003685597
- Fang, Y., Wang, X., Liu, H., & Li, T. (2019). Pareto-Optimal Reinsurance for Both the Insurer and the Reinsurer with General Premium Principles. Communications in Statistics—Theory and Methods, 48, 6134-6154. https://doi.org/10.1080/03610926.2018.1528364