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Optimal reinsuranceinvestment strategies for insurers under meanCaR criteria
1.  Lingnan (University) College, Sun Yatsen University, Guangzhou 510275, China 
2.  Lingnan (University) College/Sun Yatsen Business School, Sun Yatsen University, Guangzhou 510275, China 
References:
[1] 
S. Asmussen, B. Højgaard and M. Taksar, Optimal risk control and dividend distribution policies. Example of excessof loss reinsurance for an insurance corporation, Finance and Stochastics, 4 (2000), 299324. 
[2] 
P. Azcue and N. Muler, Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints, Insurance: Mathematics and Economics, 44 (2009), 2634. doi: 10.1016/j.insmatheco.2008.09.006. 
[3] 
L. H. Bai and J. Y. Guo, Optimal proportional reinsurance and investment with multiple risky assets and noshorting constraint, Insurance: Mathematics and Economics, 42 (2008), 968975. doi: 10.1016/j.insmatheco.2007.11.002. 
[4] 
L. H. Bai and H. Y. Zhang, Dynamic meanvariance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research, 68 (2008), 181205. doi: 10.1007/s0018600701954. 
[5] 
N. Bäuerle, Benchmark and meanvariance problems for insurers, Mathematical Methods of Operations Research, 62 (2005), 159165. 
[6] 
F. Black and A. F. Perold, Theory of constant proportion portfolio insurance, Journal of Economic Dynamics and Control, 16 (1992), 403426. doi: 10.1016/01651889(92)90043E. 
[7] 
S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing probability of ruin, Mathematics of Operations Research, 20 (1995), 937958. doi: 10.1287/moor.20.4.937. 
[8] 
Y. S. Cao and N. Q. Wan, Optimal proportional reinsurance and investment based on HamiltonJacobiBellman equation, Insurance: Mathematics and Economics, 45 (2009), 157162. doi: 10.1016/j.insmatheco.2009.05.006. 
[9] 
Ł. Delong and R. Gerrard, Meanvariance portfolio selection for a nonlife insurance company, Mathematical Methods of Operations Research, 66 (2007), 339367. doi: 10.1007/s0018600701522. 
[10] 
S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bound downside risks, Working paper, (2000). 
[11] 
S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bounded captial at risk, Mathematical Finance, 11 (2001), 365384. doi: 10.1111/14679965.00121. 
[12] 
P. Gänssler and W. Stute, "Wahrscheinlichkeitstheorie," SpringerVerlag, BerlinNew York, 1977. 
[13] 
J. Grandlle, "Aspects of Risk Theory," Springer Series in Statistics: Probability and its Applications, SpringerVerlag, New York, 1991. 
[14] 
C. Hipp and M. Plum, Optimal investment for insurers, Insurance: Mathematics and Economics, 27 (2000), 215228. doi: 10.1016/S01676687(00)000494. 
[15] 
D. Iglehart, Diffusion approximations in collective risk theory, Journal of Applied Probability, 6 (1969), 285292. 
[16] 
C. Irgens and J. Paulsen, Optimal control of risk exposure, reinsurance and investment for insurance portfolios, Insurance: Mathematics and Economics, 35 (2004), 2151. doi: 10.1016/j.insmatheco.2004.04.004. 
[17] 
R. Korn, "Optimal Portfolios," World Scientific, Singapore, 1997. 
[18] 
Z.F. Li, K. W. Ng and X.T. Deng, Continuoustime optimal portfolio selection using meanCaR models, Nonlinear Dynamics and Systems Theory, 7 (2007), 3549. 
[19] 
Z.F. Li, Y. Zeng and Y. L. Lai, Optimal timeconsistent investment and reinsurance strategies for insurers under Heston's SV model, Insurance: Mathematics and Economics, 2011. doi: 10.1016/j.insmatheco.2011.09.002. 
[20] 
Z.B. Liang, Optimal proportional reinsurance for controlled risk process which is perturbed by diffusion, Acta Mathematicae Applicatae Sinica, English Series, 23 (2007), 477488. 
[21] 
Z.B. Liang and J.Y. Guo, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23 (2007), 333350. doi: 10.1080/15326340701300894. 
[22] 
Z.B. Liang and J.Y. Guo, Upper bound for ruin probabilities under optimal investment and proportional reinsurance, Applied Stochastic Models in Business and Industry, 24 (2008), 109128. doi: 10.1002/asmb.694. 
[23] 
C. S. Liu and H. L. Yang, Optimal investment for an insurer to minimize its probability of ruin, North American Actuarial Journal, 8 (2004), 1131. 
[24] 
S.Z. Luo, Ruin minimization for insurers with borrowing constraints, North American Actuarial Journal, 12 (2009), 143174. 
[25] 
S.Z. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance: Mathematics and Economics, 42 (2008), 434444. doi: 10.1016/j.insmatheco.2007.04.002. 
[26] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime model, Review of Economics and Statistics, 51 (1969), 247256. doi: 10.2307/1926560. 
[27] 
R. C. Merton, Optimum consumption and portfolio rules in a continuoustime model, Journal of Economic Theory, 3 (1971), 373413. 
[28] 
A. F. Perold and W. F. Sharpe, Dynamic strategies for asset allocation, Financial Analyst Journal, 44 (1988), 1627. doi: 10.2469/faj.v44.n1.16. 
[29] 
S. D. Promislow and V. R. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109128. 
[30] 
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scandinavian Actuarial Journal, 1 (2001), 5568. 
[31] 
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, The Annals of Applied Probability, 12 (2002), 890907. 
[32] 
M. Taksar and C. Markussen, Optimal dynamic reinsurance policies for large insurance portfolios, Finance and Stochastics, 7 (2003), 97121. 
[33] 
Z. W. Wang, J. M. Xia and L. H. Zhang, Optimal investment for an insurer: The martingale approach, Insurance: Mathematics and Economics, 40 (2007), 322334. doi: 10.1016/j.insmatheco.2006.05.003. 
[34] 
L. Xu, R. M. Wang and D. J. Yao, On maximizing the expected terminal utility by investment and reinsurance, Journal of Industrial and Management Optimization, 4 (2008), 801815. 
[35] 
H. L. Yang and L. H. Zhang, Optimal investment for insurer with jumpdiffusion risk process, Insurance: Mathematics and Economics, 37 (2005), 615634. doi: 10.1016/j.insmatheco.2005.06.009. 
[36] 
Y. Zeng and Z. F. Li, Optimal timeconsistent investment and reinsurance policies for meanvariance insurers, Insurance: Mathematics and Economics, 49 (2011), 145154. doi: 10.1016/j.insmatheco.2011.01.001. 
[37] 
Y. Zeng, Z. F. Li and J. J. Liu, Optimal strategies of benchmark and meanvariance portfolio selection problems for insurers, Journal of Industrial and Management Optimization, 6 (2010), 483496. 
show all references
References:
[1] 
S. Asmussen, B. Højgaard and M. Taksar, Optimal risk control and dividend distribution policies. Example of excessof loss reinsurance for an insurance corporation, Finance and Stochastics, 4 (2000), 299324. 
[2] 
P. Azcue and N. Muler, Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints, Insurance: Mathematics and Economics, 44 (2009), 2634. doi: 10.1016/j.insmatheco.2008.09.006. 
[3] 
L. H. Bai and J. Y. Guo, Optimal proportional reinsurance and investment with multiple risky assets and noshorting constraint, Insurance: Mathematics and Economics, 42 (2008), 968975. doi: 10.1016/j.insmatheco.2007.11.002. 
[4] 
L. H. Bai and H. Y. Zhang, Dynamic meanvariance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research, 68 (2008), 181205. doi: 10.1007/s0018600701954. 
[5] 
N. Bäuerle, Benchmark and meanvariance problems for insurers, Mathematical Methods of Operations Research, 62 (2005), 159165. 
[6] 
F. Black and A. F. Perold, Theory of constant proportion portfolio insurance, Journal of Economic Dynamics and Control, 16 (1992), 403426. doi: 10.1016/01651889(92)90043E. 
[7] 
S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing probability of ruin, Mathematics of Operations Research, 20 (1995), 937958. doi: 10.1287/moor.20.4.937. 
[8] 
Y. S. Cao and N. Q. Wan, Optimal proportional reinsurance and investment based on HamiltonJacobiBellman equation, Insurance: Mathematics and Economics, 45 (2009), 157162. doi: 10.1016/j.insmatheco.2009.05.006. 
[9] 
Ł. Delong and R. Gerrard, Meanvariance portfolio selection for a nonlife insurance company, Mathematical Methods of Operations Research, 66 (2007), 339367. doi: 10.1007/s0018600701522. 
[10] 
S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bound downside risks, Working paper, (2000). 
[11] 
S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bounded captial at risk, Mathematical Finance, 11 (2001), 365384. doi: 10.1111/14679965.00121. 
[12] 
P. Gänssler and W. Stute, "Wahrscheinlichkeitstheorie," SpringerVerlag, BerlinNew York, 1977. 
[13] 
J. Grandlle, "Aspects of Risk Theory," Springer Series in Statistics: Probability and its Applications, SpringerVerlag, New York, 1991. 
[14] 
C. Hipp and M. Plum, Optimal investment for insurers, Insurance: Mathematics and Economics, 27 (2000), 215228. doi: 10.1016/S01676687(00)000494. 
[15] 
D. Iglehart, Diffusion approximations in collective risk theory, Journal of Applied Probability, 6 (1969), 285292. 
[16] 
C. Irgens and J. Paulsen, Optimal control of risk exposure, reinsurance and investment for insurance portfolios, Insurance: Mathematics and Economics, 35 (2004), 2151. doi: 10.1016/j.insmatheco.2004.04.004. 
[17] 
R. Korn, "Optimal Portfolios," World Scientific, Singapore, 1997. 
[18] 
Z.F. Li, K. W. Ng and X.T. Deng, Continuoustime optimal portfolio selection using meanCaR models, Nonlinear Dynamics and Systems Theory, 7 (2007), 3549. 
[19] 
Z.F. Li, Y. Zeng and Y. L. Lai, Optimal timeconsistent investment and reinsurance strategies for insurers under Heston's SV model, Insurance: Mathematics and Economics, 2011. doi: 10.1016/j.insmatheco.2011.09.002. 
[20] 
Z.B. Liang, Optimal proportional reinsurance for controlled risk process which is perturbed by diffusion, Acta Mathematicae Applicatae Sinica, English Series, 23 (2007), 477488. 
[21] 
Z.B. Liang and J.Y. Guo, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23 (2007), 333350. doi: 10.1080/15326340701300894. 
[22] 
Z.B. Liang and J.Y. Guo, Upper bound for ruin probabilities under optimal investment and proportional reinsurance, Applied Stochastic Models in Business and Industry, 24 (2008), 109128. doi: 10.1002/asmb.694. 
[23] 
C. S. Liu and H. L. Yang, Optimal investment for an insurer to minimize its probability of ruin, North American Actuarial Journal, 8 (2004), 1131. 
[24] 
S.Z. Luo, Ruin minimization for insurers with borrowing constraints, North American Actuarial Journal, 12 (2009), 143174. 
[25] 
S.Z. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance: Mathematics and Economics, 42 (2008), 434444. doi: 10.1016/j.insmatheco.2007.04.002. 
[26] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime model, Review of Economics and Statistics, 51 (1969), 247256. doi: 10.2307/1926560. 
[27] 
R. C. Merton, Optimum consumption and portfolio rules in a continuoustime model, Journal of Economic Theory, 3 (1971), 373413. 
[28] 
A. F. Perold and W. F. Sharpe, Dynamic strategies for asset allocation, Financial Analyst Journal, 44 (1988), 1627. doi: 10.2469/faj.v44.n1.16. 
[29] 
S. D. Promislow and V. R. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109128. 
[30] 
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scandinavian Actuarial Journal, 1 (2001), 5568. 
[31] 
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, The Annals of Applied Probability, 12 (2002), 890907. 
[32] 
M. Taksar and C. Markussen, Optimal dynamic reinsurance policies for large insurance portfolios, Finance and Stochastics, 7 (2003), 97121. 
[33] 
Z. W. Wang, J. M. Xia and L. H. Zhang, Optimal investment for an insurer: The martingale approach, Insurance: Mathematics and Economics, 40 (2007), 322334. doi: 10.1016/j.insmatheco.2006.05.003. 
[34] 
L. Xu, R. M. Wang and D. J. Yao, On maximizing the expected terminal utility by investment and reinsurance, Journal of Industrial and Management Optimization, 4 (2008), 801815. 
[35] 
H. L. Yang and L. H. Zhang, Optimal investment for insurer with jumpdiffusion risk process, Insurance: Mathematics and Economics, 37 (2005), 615634. doi: 10.1016/j.insmatheco.2005.06.009. 
[36] 
Y. Zeng and Z. F. Li, Optimal timeconsistent investment and reinsurance policies for meanvariance insurers, Insurance: Mathematics and Economics, 49 (2011), 145154. doi: 10.1016/j.insmatheco.2011.01.001. 
[37] 
Y. Zeng, Z. F. Li and J. J. Liu, Optimal strategies of benchmark and meanvariance portfolio selection problems for insurers, Journal of Industrial and Management Optimization, 6 (2010), 483496. 
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