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On EOQ cost models with arbitrary purchase and transportation costs
Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs
1. | School of Statistics, Qufu Normal University, Shandong 273165, China |
2. | Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China |
References:
[1] |
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1992. |
[2] |
S. Asmussen, F. Avram and M. R. Pistorius, Russian and American put options under exponential phase-type Lévy models, Stochastic Processes and their Applications, 109 (2004), 79-111.
doi: 10.1016/j.spa.2003.07.005. |
[3] |
B. Avanzi, Strategies for dividend distribution: A review, North American Actuarial Journal, 13 (2009), 217-251.
doi: 10.1080/10920277.2009.10597549. |
[4] |
B. Avanzi, E. C. K. Cheung, B. Wong and J.-K. Woo, On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency, Insurance: Mathematics and Economics, 52 (2013), 98-113.
doi: 10.1016/j.insmatheco.2012.10.008. |
[5] |
B. Avanzi and H. U. Gerber, Optimal dividends in the dual model with diffusion, ASTIN Bulletin, 38 (2008), 653-667.
doi: 10.2143/AST.38.2.2033357. |
[6] |
B. Avanzi, H. U. Gerber and E. S. W. Shiu, Optimal dividends in the dual model, Insurance: Mathematics and Economics, 41 (2007), 111-123.
doi: 10.1016/j.insmatheco.2006.10.002. |
[7] |
B. Avanzi, J. Shen and B. Wong, Optimal dividends and capital injections in the dual model with diffusion, ASTIN Bulletin, 41 (2011), 611-644.
doi: 10.2139/ssrn.1709174. |
[8] |
B. Avanzi, V. Tu and B. Wong, On optimal periodic dividend strategies in the dual model with diffusion, Insurance: Mathematics and Economics, 55 (2014), 210-224.
doi: 10.1016/j.insmatheco.2014.01.005. |
[9] |
P. Azcue and N. Muler, Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model, Mathematical Finance, 15 (2005), 261-308.
doi: 10.1111/j.0960-1627.2005.00220.x. |
[10] |
E. Bayraktar and M. Egami, Optimizing venture capital investments in a jump diffusion model, Mathematical Methods of Operations Research, 67 (2008), 21-42.
doi: 10.1007/s00186-007-0181-x. |
[11] |
E. Bayraktar, A. E. Kyprianou and K. Yamazaki, On optimal dividends in the dual model, ASTIN Bulletin, 43 (2013), 359-372.
doi: 10.1017/asb.2013.17. |
[12] |
E. Bayraktar, A. E. Kyprianou and K. Yamazaki, Optimal dividends in the dual model under transaction costs, Insurance: Mathematics and Economics, 54 (2014), 133-143.
doi: 10.1016/j.insmatheco.2013.11.007. |
[13] |
E. C. K. Cheung and S. Drekic, Dividend moments in the dual model: Exact and approximate approaches, ASTIN Bulletin, 38 (2008), 399-422.
doi: 10.2143/AST.38.2.2033347. |
[14] |
H. Dai, Z. Liu and N. Luan, Optimal dividend strategies in a dual model with capital injections, Mathematical Methods of Operations Research, 72 (2010), 129-143.
doi: 10.1007/s00186-010-0312-7. |
[15] |
H. Dai, Z. Liu and N. Luan, Optimal financing and dividend control in the dual model, Mathematical and Computer Modelling, 53 (2011), 1921-1928.
doi: 10.1016/j.mcm.2011.01.019. |
[16] |
B. De Finetti, Su un'impostazion alternativa dell teoria collecttiva del rischio, Transactions of the XVth International Congress of Actuaries, 2 (1957), 433-443. |
[17] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Applications of Mathematics, Springer-Verlag, New York, 1993. |
[18] |
L. He and Z. Liang, Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs, Insurance: Mathematics and Economics, 44 (2009), 88-94.
doi: 10.1016/j.insmatheco.2008.10.001. |
[19] |
S. Jaschke, A note on the inhomogeneous linear stochastic differential equation, Insurance: Mathematics and Economics, 32 (2003), 461-464.
doi: 10.1016/S0167-6687(03)00134-3. |
[20] |
N. Kulenko and H. Schmidli, Optimal dividend strategies in a Cramér-Lundberg model with capital injections, Insurance: Mathematics and Economics, 43 (2008), 270-278.
doi: 10.1016/j.insmatheco.2008.05.013. |
[21] |
K. Miyasawa, An economic survival game, Journal of the Operations Research Society of Japan, 4 (1962), 95-113. |
[22] |
H. Schmidli, Stochastic Control in Insurance, Springer, New York, 2008. |
[23] |
D. J. Yao, H. L. Yang and R. M. Wang, Optimal financing and dividend strategies in a dual model with proportional costs, Journal of Industrial and Management Optimization, 6 (2010), 761-777.
doi: 10.3934/jimo.2010.6.761. |
[24] |
D. J. Yao, H. L. Yang and R. W. Wang, Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs, European Journal of Operational Research, 211 (2011), 568-576.
doi: 10.1016/j.ejor.2011.01.015. |
[25] |
D. J. Yao, R. W. Wang and L. Xu, Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model, Journal of Industrial and Management Optimization, 10 (2014), 1235-1259.
doi: 10.3934/jimo.2014.10.1235. |
[26] |
C. C. Yin and Y. Z. Wen, Optimal dividends problem with a terminal value for spectrally positive Lévy processes, Insurance: Mathematics and Economics, 53 (2013), 769-773.
doi: 10.1016/j.insmatheco.2013.09.019. |
[27] |
C. C. Yin and Y. Z. Wen, An extension of Paulsen-Gjessing's risk model with stochastic return on investments, Insurance: Mathematics and Economics, 52 (2013), 469-476.
doi: 10.1016/j.insmatheco.2013.02.014. |
[28] |
C. C. Yin, Y. Z. Wen and Y. X. Zhao, On the optimal dividend problem for a spectrally positive Lévy process, ASTIN Bulletin, 44 (2014), 635-651.
doi: 10.1017/asb.2014.12. |
[29] |
Z. M. Zhang, On a risk model with randomized dividend-decision times, Journal of Industrial and Management Optimization, 10 (2014), 1041-1058.
doi: 10.3934/jimo.2014.10.1041. |
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1992. |
[2] |
S. Asmussen, F. Avram and M. R. Pistorius, Russian and American put options under exponential phase-type Lévy models, Stochastic Processes and their Applications, 109 (2004), 79-111.
doi: 10.1016/j.spa.2003.07.005. |
[3] |
B. Avanzi, Strategies for dividend distribution: A review, North American Actuarial Journal, 13 (2009), 217-251.
doi: 10.1080/10920277.2009.10597549. |
[4] |
B. Avanzi, E. C. K. Cheung, B. Wong and J.-K. Woo, On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency, Insurance: Mathematics and Economics, 52 (2013), 98-113.
doi: 10.1016/j.insmatheco.2012.10.008. |
[5] |
B. Avanzi and H. U. Gerber, Optimal dividends in the dual model with diffusion, ASTIN Bulletin, 38 (2008), 653-667.
doi: 10.2143/AST.38.2.2033357. |
[6] |
B. Avanzi, H. U. Gerber and E. S. W. Shiu, Optimal dividends in the dual model, Insurance: Mathematics and Economics, 41 (2007), 111-123.
doi: 10.1016/j.insmatheco.2006.10.002. |
[7] |
B. Avanzi, J. Shen and B. Wong, Optimal dividends and capital injections in the dual model with diffusion, ASTIN Bulletin, 41 (2011), 611-644.
doi: 10.2139/ssrn.1709174. |
[8] |
B. Avanzi, V. Tu and B. Wong, On optimal periodic dividend strategies in the dual model with diffusion, Insurance: Mathematics and Economics, 55 (2014), 210-224.
doi: 10.1016/j.insmatheco.2014.01.005. |
[9] |
P. Azcue and N. Muler, Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model, Mathematical Finance, 15 (2005), 261-308.
doi: 10.1111/j.0960-1627.2005.00220.x. |
[10] |
E. Bayraktar and M. Egami, Optimizing venture capital investments in a jump diffusion model, Mathematical Methods of Operations Research, 67 (2008), 21-42.
doi: 10.1007/s00186-007-0181-x. |
[11] |
E. Bayraktar, A. E. Kyprianou and K. Yamazaki, On optimal dividends in the dual model, ASTIN Bulletin, 43 (2013), 359-372.
doi: 10.1017/asb.2013.17. |
[12] |
E. Bayraktar, A. E. Kyprianou and K. Yamazaki, Optimal dividends in the dual model under transaction costs, Insurance: Mathematics and Economics, 54 (2014), 133-143.
doi: 10.1016/j.insmatheco.2013.11.007. |
[13] |
E. C. K. Cheung and S. Drekic, Dividend moments in the dual model: Exact and approximate approaches, ASTIN Bulletin, 38 (2008), 399-422.
doi: 10.2143/AST.38.2.2033347. |
[14] |
H. Dai, Z. Liu and N. Luan, Optimal dividend strategies in a dual model with capital injections, Mathematical Methods of Operations Research, 72 (2010), 129-143.
doi: 10.1007/s00186-010-0312-7. |
[15] |
H. Dai, Z. Liu and N. Luan, Optimal financing and dividend control in the dual model, Mathematical and Computer Modelling, 53 (2011), 1921-1928.
doi: 10.1016/j.mcm.2011.01.019. |
[16] |
B. De Finetti, Su un'impostazion alternativa dell teoria collecttiva del rischio, Transactions of the XVth International Congress of Actuaries, 2 (1957), 433-443. |
[17] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Applications of Mathematics, Springer-Verlag, New York, 1993. |
[18] |
L. He and Z. Liang, Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs, Insurance: Mathematics and Economics, 44 (2009), 88-94.
doi: 10.1016/j.insmatheco.2008.10.001. |
[19] |
S. Jaschke, A note on the inhomogeneous linear stochastic differential equation, Insurance: Mathematics and Economics, 32 (2003), 461-464.
doi: 10.1016/S0167-6687(03)00134-3. |
[20] |
N. Kulenko and H. Schmidli, Optimal dividend strategies in a Cramér-Lundberg model with capital injections, Insurance: Mathematics and Economics, 43 (2008), 270-278.
doi: 10.1016/j.insmatheco.2008.05.013. |
[21] |
K. Miyasawa, An economic survival game, Journal of the Operations Research Society of Japan, 4 (1962), 95-113. |
[22] |
H. Schmidli, Stochastic Control in Insurance, Springer, New York, 2008. |
[23] |
D. J. Yao, H. L. Yang and R. M. Wang, Optimal financing and dividend strategies in a dual model with proportional costs, Journal of Industrial and Management Optimization, 6 (2010), 761-777.
doi: 10.3934/jimo.2010.6.761. |
[24] |
D. J. Yao, H. L. Yang and R. W. Wang, Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs, European Journal of Operational Research, 211 (2011), 568-576.
doi: 10.1016/j.ejor.2011.01.015. |
[25] |
D. J. Yao, R. W. Wang and L. Xu, Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model, Journal of Industrial and Management Optimization, 10 (2014), 1235-1259.
doi: 10.3934/jimo.2014.10.1235. |
[26] |
C. C. Yin and Y. Z. Wen, Optimal dividends problem with a terminal value for spectrally positive Lévy processes, Insurance: Mathematics and Economics, 53 (2013), 769-773.
doi: 10.1016/j.insmatheco.2013.09.019. |
[27] |
C. C. Yin and Y. Z. Wen, An extension of Paulsen-Gjessing's risk model with stochastic return on investments, Insurance: Mathematics and Economics, 52 (2013), 469-476.
doi: 10.1016/j.insmatheco.2013.02.014. |
[28] |
C. C. Yin, Y. Z. Wen and Y. X. Zhao, On the optimal dividend problem for a spectrally positive Lévy process, ASTIN Bulletin, 44 (2014), 635-651.
doi: 10.1017/asb.2014.12. |
[29] |
Z. M. Zhang, On a risk model with randomized dividend-decision times, Journal of Industrial and Management Optimization, 10 (2014), 1041-1058.
doi: 10.3934/jimo.2014.10.1041. |
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