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Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission
1. | School of Finance, The Center of Cooperative Innovation for Modern Service Industry, Nanjing University of Finance and Economics, Nanjing 210023 |
2. | School of Finance and Statistics, Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241 |
3. | School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui, 241003 |
References:
[1] |
B. Avanzi, J. Shen and B. Wong, Optimal dividends and capital injections in the dual model with diffusion,, ASTIN Bulletin, 41 (2011), 611.
doi: 10.2139/ssrn.1709174. |
[2] |
F. Avram, Z. Palmowski and M. R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process,, The Annals of Applied Probability, 17 (2007), 156.
doi: 10.1214/105051606000000709. |
[3] |
A. Cadenillas and F. Zapatero, Optimal central bank intervention in the foreign exchange market,, Journal of Economic Theory, 87 (1999), 218.
doi: 10.1006/jeth.1999.2523. |
[4] |
J. Cai, H. U. Gerber and H. Yang, Optimal dividends in an Ornstein-Uhlenbeck type model with credit and debit interest,, North American Actuarial Journal, 10 (2006), 94.
doi: 10.1080/10920277.2006.10596250. |
[5] |
H. U. Gerber and E. S. W. Shiu, Geometric Brownian motion models for assets and liabilities from pension funding to optimal dividends,, North American Actuarial Journal, 7 (2003), 37.
doi: 10.1080/10920277.2003.10596099. |
[6] |
H. U. Gerber and E. S. W. Shiu, Optimal dividends: Analysis with Brownian motion,, North American Actuarial Journal, 8 (2004), 1.
doi: 10.1080/10920277.2004.10596125. |
[7] |
B. Høgaard and M. Taksar, Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy,, Quantitative Finance, 4 (2004), 315.
doi: 10.1088/1469-7688/4/3/007. |
[8] |
N. Kulenko and H. Schimidli, Optimal dividend strategy in a Cramér-Lundberg model with capital injections,, Insurance: Mathematics and Economics, 43 (2008), 270.
doi: 10.1016/j.insmatheco.2008.05.013. |
[9] |
K. S. Leung, Y. K. Kwok and S. Y. Leung, Finite-time dividend-ruin models,, Insurance: Mathematics and Economics, 42 (2008), 154.
doi: 10.1016/j.insmatheco.2007.01.014. |
[10] |
P. L. Lions and A. S. Sznitman, Stochastic differential equations with reflecting boundary conditions,, Communications on Pure and Applied Mathematics, 37 (1984), 511.
doi: 10.1002/cpa.3160370408. |
[11] |
A. Løkka and M. Zervos, Optimal dividend and issuance of equity policies in the presence of proportional costs,, Insurance: Mathematics and Economics, 42 (2008), 954.
doi: 10.1016/j.insmatheco.2007.10.013. |
[12] |
H. Meng and T. Siu, On optimal reinsurance, dividend and reinvestment strategies,, Economic Modelling, 28 (2011), 211.
doi: 10.1016/j.econmod.2010.09.009. |
[13] |
M. Ohnishi and M. Tsujimura, An impulse control of a geometric Brownian motion with quadratic costs,, European Journal of Operational Research, 168 (2006), 311.
doi: 10.1016/j.ejor.2004.07.006. |
[14] |
J. Paulsen, Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs,, Advances in Applied Probability, 39 (2007), 669.
doi: 10.1239/aap/1189518633. |
[15] |
J. Paulsen, Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs,, SIAM Journal on Control and Optimization, 47 (2008), 2201.
doi: 10.1137/070691632. |
[16] |
S. P. Sethi and M. Taksar, Optimal financing of a corporation subject to random retures,, Mathematical Finance, 12 (2002), 155.
doi: 10.1111/1467-9965.t01-2-02002. |
[17] |
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers,, SIAM Journal on Control and Optimization, 22 (1984), 55.
doi: 10.1137/0322005. |
[18] |
D. Yao, H. Yang and R. Wang, Optimal financing and dividend strategies in a dual model with proportional costs,, Journal of Industrial and Management Optimization, 6 (2010), 761.
doi: 10.3934/jimo.2010.6.761. |
[19] |
D. Yao, H. Yang and R. Wang, Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle,, Economic Modelling, 37 (2014), 53.
doi: 10.1016/j.econmod.2013.10.026. |
show all references
References:
[1] |
B. Avanzi, J. Shen and B. Wong, Optimal dividends and capital injections in the dual model with diffusion,, ASTIN Bulletin, 41 (2011), 611.
doi: 10.2139/ssrn.1709174. |
[2] |
F. Avram, Z. Palmowski and M. R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process,, The Annals of Applied Probability, 17 (2007), 156.
doi: 10.1214/105051606000000709. |
[3] |
A. Cadenillas and F. Zapatero, Optimal central bank intervention in the foreign exchange market,, Journal of Economic Theory, 87 (1999), 218.
doi: 10.1006/jeth.1999.2523. |
[4] |
J. Cai, H. U. Gerber and H. Yang, Optimal dividends in an Ornstein-Uhlenbeck type model with credit and debit interest,, North American Actuarial Journal, 10 (2006), 94.
doi: 10.1080/10920277.2006.10596250. |
[5] |
H. U. Gerber and E. S. W. Shiu, Geometric Brownian motion models for assets and liabilities from pension funding to optimal dividends,, North American Actuarial Journal, 7 (2003), 37.
doi: 10.1080/10920277.2003.10596099. |
[6] |
H. U. Gerber and E. S. W. Shiu, Optimal dividends: Analysis with Brownian motion,, North American Actuarial Journal, 8 (2004), 1.
doi: 10.1080/10920277.2004.10596125. |
[7] |
B. Høgaard and M. Taksar, Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy,, Quantitative Finance, 4 (2004), 315.
doi: 10.1088/1469-7688/4/3/007. |
[8] |
N. Kulenko and H. Schimidli, Optimal dividend strategy in a Cramér-Lundberg model with capital injections,, Insurance: Mathematics and Economics, 43 (2008), 270.
doi: 10.1016/j.insmatheco.2008.05.013. |
[9] |
K. S. Leung, Y. K. Kwok and S. Y. Leung, Finite-time dividend-ruin models,, Insurance: Mathematics and Economics, 42 (2008), 154.
doi: 10.1016/j.insmatheco.2007.01.014. |
[10] |
P. L. Lions and A. S. Sznitman, Stochastic differential equations with reflecting boundary conditions,, Communications on Pure and Applied Mathematics, 37 (1984), 511.
doi: 10.1002/cpa.3160370408. |
[11] |
A. Løkka and M. Zervos, Optimal dividend and issuance of equity policies in the presence of proportional costs,, Insurance: Mathematics and Economics, 42 (2008), 954.
doi: 10.1016/j.insmatheco.2007.10.013. |
[12] |
H. Meng and T. Siu, On optimal reinsurance, dividend and reinvestment strategies,, Economic Modelling, 28 (2011), 211.
doi: 10.1016/j.econmod.2010.09.009. |
[13] |
M. Ohnishi and M. Tsujimura, An impulse control of a geometric Brownian motion with quadratic costs,, European Journal of Operational Research, 168 (2006), 311.
doi: 10.1016/j.ejor.2004.07.006. |
[14] |
J. Paulsen, Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs,, Advances in Applied Probability, 39 (2007), 669.
doi: 10.1239/aap/1189518633. |
[15] |
J. Paulsen, Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs,, SIAM Journal on Control and Optimization, 47 (2008), 2201.
doi: 10.1137/070691632. |
[16] |
S. P. Sethi and M. Taksar, Optimal financing of a corporation subject to random retures,, Mathematical Finance, 12 (2002), 155.
doi: 10.1111/1467-9965.t01-2-02002. |
[17] |
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers,, SIAM Journal on Control and Optimization, 22 (1984), 55.
doi: 10.1137/0322005. |
[18] |
D. Yao, H. Yang and R. Wang, Optimal financing and dividend strategies in a dual model with proportional costs,, Journal of Industrial and Management Optimization, 6 (2010), 761.
doi: 10.3934/jimo.2010.6.761. |
[19] |
D. Yao, H. Yang and R. Wang, Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle,, Economic Modelling, 37 (2014), 53.
doi: 10.1016/j.econmod.2013.10.026. |
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