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Optimal layer reinsurance on the maximization of the adjustment coefficient
1. | School of Mathematical Sciences, Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, China, China |
References:
[1] |
S. Asmussen, Ruin probabilities, World Scientific Press, Singapore, 2000.
doi: 10.1142/9789812779311. |
[2] |
E. Bayraktar and V. Young, Minimizing the probability of lifetime ruin under borrowing constraints, Insurance: Mathematics and Economics, 41 (2007), 196-221.
doi: 10.1016/j.insmatheco.2006.10.015. |
[3] |
C. Bernard and W. Tian, Optimal reinsurance arrangements under tail risk measures, Journal of Risk and Insurance, 76 (2009), 709-725. |
[4] |
S. Browne, Optimal investment policies for a firm with random risk process: exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20 (1995), 937-958.
doi: 10.1287/moor.20.4.937. |
[5] |
J. Cai and K. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, ASTIN Bulletin, 37 (2007), 93-112.
doi: 10.2143/AST.37.1.2020800. |
[6] |
J. Cai, K. Tan, C. Weng and Y. Zhang, Optimal reinsurance under VaR and CTE risk measures, Insurance: Mathematics and Economics, 43 (2008), 185-196.
doi: 10.1016/j.insmatheco.2008.05.011. |
[7] |
M. Centeno, Dependent risks and excess of loss reinsurance, Insurance: Mathematics and Economics, 37 (2005), 229-238.
doi: 10.1016/j.insmatheco.2004.12.001. |
[8] |
M. Centeno and O. Simũes, Combining quota-share and excess of loss treaties on the reinsurance of n independent risks, ASTIN Bulletin, 21 (2002), 41-55. |
[9] |
H. Gerber, An Introduction to Mathematical Risk Theory, In: S. S. Huebner Foundation Monograph, Series No. 8. Irwin, Homewood, Illinois, 1979. |
[10] |
J. Grandell, Aspects of Risk Theory, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4613-9058-9. |
[11] |
M. Guerra and M. Centeno, Optimal reinsurance for variance related premium calculation principles, ASTIN Bulletin, 40 (2010), 97-121.
doi: 10.2143/AST.40.1.2049220. |
[12] |
M. Hald and H. Schmidli, On the maximization of the adjustment coefficient under proportioal reinsurance, ASTIN Bulletin, 34 (2004), 75-83.
doi: 10.2143/AST.34.1.504955. |
[13] |
C. Irgens and J. Paulsen, Optimal control of risk exposure, reinsurance and investments for insurance portfolios, Insurance: Mathematics and Economics, 35 (2004), 21-51.
doi: 10.1016/j.insmatheco.2004.04.004. |
[14] |
M. Kaluszka, Optimal reinsurance under mean-variance premium principles, Insurance: Mathematics and Economics, 28 (2001), 61-67.
doi: 10.1016/S0167-6687(00)00066-4. |
[15] |
M. Kaluszka, Mean-variance optimal reinsurance arrangements, Scandinavian Actuarial Journal, 1 (2004), 28-41.
doi: 10.1080/03461230410019222. |
[16] |
Z. Liang and E. Bayraktar, Optimal proportional reinsurance and investment with unobservable claim sizes and intensity, Insurance: Mathematics and Economics, 55 (2014), 156-166.
doi: 10.1016/j.insmatheco.2014.01.011. |
[17] |
Z. Liang and J. Guo, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23 (2007), 333-350.
doi: 10.1080/15326340701300894. |
[18] |
Z. Liang and J. Guo, Ruin probabilities under optimal combining quota-share and excess of loss reinsurance, Acta Mathematica Sinica, Chinese Series, 9 (2010), 858-870. |
[19] |
Z. Liang and V. Young, Dividends and reinsurance under a penalty for ruin, Insurance: Mathematics and Economics, 50 (2012), 437-445. |
[20] |
S. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance: Mathematics and Economics, 42 (2008), 434-444.
doi: 10.1016/j.insmatheco.2007.04.002. |
[21] |
D. Promislow and V. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109-128. |
[22] |
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scandinavian Actuarial Journal, 1 (2001), 55-68.
doi: 10.1080/034612301750077338. |
[23] |
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, Annals of Applied Probability, 12 (2002), 890-907.
doi: 10.1214/aoap/1031863173. |
[24] |
X. Zhang, M. Zhou and J. Guo, Optimal combinational quota-share and excess of loss reinsurance policies in a dynamic setting, Applied Stochastic Model in Business and Industry, 23 (2007), 63-71.
doi: 10.1002/asmb.637. |
show all references
References:
[1] |
S. Asmussen, Ruin probabilities, World Scientific Press, Singapore, 2000.
doi: 10.1142/9789812779311. |
[2] |
E. Bayraktar and V. Young, Minimizing the probability of lifetime ruin under borrowing constraints, Insurance: Mathematics and Economics, 41 (2007), 196-221.
doi: 10.1016/j.insmatheco.2006.10.015. |
[3] |
C. Bernard and W. Tian, Optimal reinsurance arrangements under tail risk measures, Journal of Risk and Insurance, 76 (2009), 709-725. |
[4] |
S. Browne, Optimal investment policies for a firm with random risk process: exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20 (1995), 937-958.
doi: 10.1287/moor.20.4.937. |
[5] |
J. Cai and K. Tan, Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, ASTIN Bulletin, 37 (2007), 93-112.
doi: 10.2143/AST.37.1.2020800. |
[6] |
J. Cai, K. Tan, C. Weng and Y. Zhang, Optimal reinsurance under VaR and CTE risk measures, Insurance: Mathematics and Economics, 43 (2008), 185-196.
doi: 10.1016/j.insmatheco.2008.05.011. |
[7] |
M. Centeno, Dependent risks and excess of loss reinsurance, Insurance: Mathematics and Economics, 37 (2005), 229-238.
doi: 10.1016/j.insmatheco.2004.12.001. |
[8] |
M. Centeno and O. Simũes, Combining quota-share and excess of loss treaties on the reinsurance of n independent risks, ASTIN Bulletin, 21 (2002), 41-55. |
[9] |
H. Gerber, An Introduction to Mathematical Risk Theory, In: S. S. Huebner Foundation Monograph, Series No. 8. Irwin, Homewood, Illinois, 1979. |
[10] |
J. Grandell, Aspects of Risk Theory, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4613-9058-9. |
[11] |
M. Guerra and M. Centeno, Optimal reinsurance for variance related premium calculation principles, ASTIN Bulletin, 40 (2010), 97-121.
doi: 10.2143/AST.40.1.2049220. |
[12] |
M. Hald and H. Schmidli, On the maximization of the adjustment coefficient under proportioal reinsurance, ASTIN Bulletin, 34 (2004), 75-83.
doi: 10.2143/AST.34.1.504955. |
[13] |
C. Irgens and J. Paulsen, Optimal control of risk exposure, reinsurance and investments for insurance portfolios, Insurance: Mathematics and Economics, 35 (2004), 21-51.
doi: 10.1016/j.insmatheco.2004.04.004. |
[14] |
M. Kaluszka, Optimal reinsurance under mean-variance premium principles, Insurance: Mathematics and Economics, 28 (2001), 61-67.
doi: 10.1016/S0167-6687(00)00066-4. |
[15] |
M. Kaluszka, Mean-variance optimal reinsurance arrangements, Scandinavian Actuarial Journal, 1 (2004), 28-41.
doi: 10.1080/03461230410019222. |
[16] |
Z. Liang and E. Bayraktar, Optimal proportional reinsurance and investment with unobservable claim sizes and intensity, Insurance: Mathematics and Economics, 55 (2014), 156-166.
doi: 10.1016/j.insmatheco.2014.01.011. |
[17] |
Z. Liang and J. Guo, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23 (2007), 333-350.
doi: 10.1080/15326340701300894. |
[18] |
Z. Liang and J. Guo, Ruin probabilities under optimal combining quota-share and excess of loss reinsurance, Acta Mathematica Sinica, Chinese Series, 9 (2010), 858-870. |
[19] |
Z. Liang and V. Young, Dividends and reinsurance under a penalty for ruin, Insurance: Mathematics and Economics, 50 (2012), 437-445. |
[20] |
S. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance: Mathematics and Economics, 42 (2008), 434-444.
doi: 10.1016/j.insmatheco.2007.04.002. |
[21] |
D. Promislow and V. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109-128. |
[22] |
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scandinavian Actuarial Journal, 1 (2001), 55-68.
doi: 10.1080/034612301750077338. |
[23] |
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, Annals of Applied Probability, 12 (2002), 890-907.
doi: 10.1214/aoap/1031863173. |
[24] |
X. Zhang, M. Zhou and J. Guo, Optimal combinational quota-share and excess of loss reinsurance policies in a dynamic setting, Applied Stochastic Model in Business and Industry, 23 (2007), 63-71.
doi: 10.1002/asmb.637. |
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