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On the fast solution of evolution equations with a rapidly decaying source term
Numerical methods for dividend optimization using regime-switching jump-diffusion models
1. | Department of Mathematics, Wayne State University, Detroit, Michigan 48202, United States, United States |
2. | Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |
References:
[1] |
S. Asmussen and M. Taksar, Controlled diffusion models for optimal dividend pay-out, Insurance: Math. and Economics, 20 (1997), 1-15.
doi: 10.1016/S0167-6687(96)00017-0. |
[2] |
S. Asmussen, B. Høgaard and M. Taksar, Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation, DFinance and Stochastics, 4 (2000), 299-324.
doi: 10.1007/s007800050075. |
[3] |
A. Cadenillas, T. Choulli, M. Taksar and L. Zhang, Classical and impulse stochastic control for the optimization of the dividend and risk policies of an insurance firm, Mathematical Finance, 16 (2006), 181-202.
doi: 10.1111/j.1467-9965.2006.00267.x. |
[4] |
P. Chen, H. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: a continuous-time model, Insurance: Math. Economics, 43 (2008), 456-465.
doi: 10.1016/j.insmatheco.2008.09.001. |
[5] |
B. De Finetti, Su unimpostazione alternativa della teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, 2 (1957), 433-443. |
[6] |
R. J. Elliott and T. K. Siu, Robust optimal portfolio choice under Markovian regime-switching model, Methodology and Computing in Applied Probability, 11 (2009), 145-157.
doi: 10.1007/s11009-008-9085-3. |
[7] |
H. Gerber, Games of economic survival with discrete- and continuous-income processes, Operations Res., 20 (1972), 37-45.
doi: 10.1287/opre.20.1.37. |
[8] |
H. Gerber, "An Introduction to Mathematical Risk Theory," in "Huebner Foundation Monograph 8" Distributed by Richard D. Irwin, Homewood, IL, 1979. |
[9] |
H. Gerber and E. Shiu, Optimal dividends: Analysis with Brownian motion, North American Actuarial Journal, 8 (2004), 1-20. |
[10] |
H. Gerber and E. Shiu, On optimal dividend strategies in the compound Poisson model, North American Actuarial Journal, 10 (2006), 76-93. |
[11] |
Z. Jiang and M. Pistorius, Optimal dividend distribution under Markov regime switching, Working paper, (2008). arXiv:0812.4978 |
[12] |
H. J. Kushner and P. Dupuis, "Numerical Methods for Stochastic Control Problems in Continuous Time," 2nd edition, Springer, New York, 2001. |
[13] |
C. F. Lee and S. W. Forbes, Dividend policy, Equity value, and cost of capital estimates in the property and liability insurance industry, J. Risk Insurance, 47 (1980), 205-222.
doi: 10.2307/252328. |
[14] |
H. Schmidli, "Stochastic Control in Insurance," Springer Verlag, 2008. |
[15] |
Q. S. Song, G. Yin and Z. Zhang, Numerical method for controlled regime-switching diffusions and regime-switching jump diffusions, Automatica, 42 (2006), 1147-1157.
doi: 10.1016/j.automatica.2006.03.016. |
[16] |
L. Sotomayor and A. Cadenillas, Classical, singular, and impulse stochastic control for the optimal dividend policy when there is regime switching, Preprint, (2008), Download at http://papers.ssrn.com/sol3/papers.cfm?abstract-id=1139444. |
[17] |
J. Wei, H. Yang and R. Wang, Optimal reinsurance and dividend strategies under the Markov-Modulated insurance risk model, Stochastic Analysis and Applications, 28 (2010), 1078-1105.
doi: 10.1080/07362994.2010.515488. |
[18] |
J. Wei, H. Yang and R. Wang, Classical and impulse control for the optimization of dividend and proportional reinsurance policies with regime switching, Journal of Optimization Theory and Applications, 147 (2010), 358-377.
doi: 10.1007/s10957-010-9726-x. |
[19] |
G. Yin, Q. Zhang and G. Badowski, Discrete-time singularly perturbed Markov chains: Aggregation, occupation measures, and switching diffusion limit, Adv. Appl. Probab., 35 (2003), 449-476.
doi: 10.1239/aap/1051201656. |
[20] |
G. Yin and C. Zhu, "Hybrid Switching Diffusions: Properties and Applications," Springer, New York, 2010.
doi: 10.1007/978-1-4419-1105-6. |
[21] |
Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Control Optim., 40 (2001), 64-87.
doi: 10.1137/S0363012999356325. |
[22] |
X. Y. Zhou and G. Yin, Markowitz mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim., 42 (2003), 1466-1482.
doi: 10.1137/S0363012902405583. |
show all references
References:
[1] |
S. Asmussen and M. Taksar, Controlled diffusion models for optimal dividend pay-out, Insurance: Math. and Economics, 20 (1997), 1-15.
doi: 10.1016/S0167-6687(96)00017-0. |
[2] |
S. Asmussen, B. Høgaard and M. Taksar, Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation, DFinance and Stochastics, 4 (2000), 299-324.
doi: 10.1007/s007800050075. |
[3] |
A. Cadenillas, T. Choulli, M. Taksar and L. Zhang, Classical and impulse stochastic control for the optimization of the dividend and risk policies of an insurance firm, Mathematical Finance, 16 (2006), 181-202.
doi: 10.1111/j.1467-9965.2006.00267.x. |
[4] |
P. Chen, H. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: a continuous-time model, Insurance: Math. Economics, 43 (2008), 456-465.
doi: 10.1016/j.insmatheco.2008.09.001. |
[5] |
B. De Finetti, Su unimpostazione alternativa della teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, 2 (1957), 433-443. |
[6] |
R. J. Elliott and T. K. Siu, Robust optimal portfolio choice under Markovian regime-switching model, Methodology and Computing in Applied Probability, 11 (2009), 145-157.
doi: 10.1007/s11009-008-9085-3. |
[7] |
H. Gerber, Games of economic survival with discrete- and continuous-income processes, Operations Res., 20 (1972), 37-45.
doi: 10.1287/opre.20.1.37. |
[8] |
H. Gerber, "An Introduction to Mathematical Risk Theory," in "Huebner Foundation Monograph 8" Distributed by Richard D. Irwin, Homewood, IL, 1979. |
[9] |
H. Gerber and E. Shiu, Optimal dividends: Analysis with Brownian motion, North American Actuarial Journal, 8 (2004), 1-20. |
[10] |
H. Gerber and E. Shiu, On optimal dividend strategies in the compound Poisson model, North American Actuarial Journal, 10 (2006), 76-93. |
[11] |
Z. Jiang and M. Pistorius, Optimal dividend distribution under Markov regime switching, Working paper, (2008). arXiv:0812.4978 |
[12] |
H. J. Kushner and P. Dupuis, "Numerical Methods for Stochastic Control Problems in Continuous Time," 2nd edition, Springer, New York, 2001. |
[13] |
C. F. Lee and S. W. Forbes, Dividend policy, Equity value, and cost of capital estimates in the property and liability insurance industry, J. Risk Insurance, 47 (1980), 205-222.
doi: 10.2307/252328. |
[14] |
H. Schmidli, "Stochastic Control in Insurance," Springer Verlag, 2008. |
[15] |
Q. S. Song, G. Yin and Z. Zhang, Numerical method for controlled regime-switching diffusions and regime-switching jump diffusions, Automatica, 42 (2006), 1147-1157.
doi: 10.1016/j.automatica.2006.03.016. |
[16] |
L. Sotomayor and A. Cadenillas, Classical, singular, and impulse stochastic control for the optimal dividend policy when there is regime switching, Preprint, (2008), Download at http://papers.ssrn.com/sol3/papers.cfm?abstract-id=1139444. |
[17] |
J. Wei, H. Yang and R. Wang, Optimal reinsurance and dividend strategies under the Markov-Modulated insurance risk model, Stochastic Analysis and Applications, 28 (2010), 1078-1105.
doi: 10.1080/07362994.2010.515488. |
[18] |
J. Wei, H. Yang and R. Wang, Classical and impulse control for the optimization of dividend and proportional reinsurance policies with regime switching, Journal of Optimization Theory and Applications, 147 (2010), 358-377.
doi: 10.1007/s10957-010-9726-x. |
[19] |
G. Yin, Q. Zhang and G. Badowski, Discrete-time singularly perturbed Markov chains: Aggregation, occupation measures, and switching diffusion limit, Adv. Appl. Probab., 35 (2003), 449-476.
doi: 10.1239/aap/1051201656. |
[20] |
G. Yin and C. Zhu, "Hybrid Switching Diffusions: Properties and Applications," Springer, New York, 2010.
doi: 10.1007/978-1-4419-1105-6. |
[21] |
Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Control Optim., 40 (2001), 64-87.
doi: 10.1137/S0363012999356325. |
[22] |
X. Y. Zhou and G. Yin, Markowitz mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim., 42 (2003), 1466-1482.
doi: 10.1137/S0363012902405583. |
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