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谱正Lévy过程下的Ratchet分红策略与Barrier策略的混合研究
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Abstract:
本文主要研究谱正Lévy过程下的混合分红策略。对公司的盈余过程进行如下两种策略的混合：首先让其执行Ratchet分红策略；而后待盈余水平到达预先设置的高度界限时，立即执行Barrier分红策略，将所有投资收益全部分红给公司股东。文章主要结果是得出了这种混合策略下的累积折现期望分红值函数。
This paper mainly studies the mixed dividend strategy under the positive Lévy process. The earnings process of the company is a mix of the following two strategies: First let them execute the Ratchet dividend strategy. And then execute the Barrier dividend strategy immediately after the surplus level reaches the preset high limit. Distribute all investment income to the shareholders of the company. Finally, the cumulative discounted expected dividend value function under the mixed strategy is obtained.
| [1] | Gerber, H.U. and Shiu, E.S.W. (2004) Optimal Dividends: Analysis with Brownian Motion. North American Actuarial Journal, 8, 1-20. https://doi.org/10.1080/10920277.2004.10596125 |
| [2] | Klüppelberg, C., Kyprianou, A. and Maller, R. (2004) Ruin Probabilities and Overshoots for General Lévy Insurance Risk Process. The Annals of Applied Probability, 14, 1766-1801. https://doi.org/10.1214/105051604000000927 |
| [3] | Péreza, J. and Yamazaki, K. (2017) On the Optimality of Periodic Barrier Strategies for a Spectrally Positive Lévy Process. Insurance: Mathematics and Economics, 77, 1-13. https://doi.org/10.1016/j.insmatheco.2017.08.001 |
| [4] | Zhao, Y.X. and Chen, P. (2017) Optimal Periodic Dividend and Capital Injection Problem for Spectrally Positive Lévy Processes. Insurance: Mathematics and Economics, 74, 135-146. https://doi.org/10.1016/j.insmatheco.2017.03.006 |
| [5] | Afonso, L.B., Cardoso, R.M.R. and Egidio dos Reis, A.D. (2013) Dividend Problems in the Dual Risk Model. Insurance: Mathematics and Economics, 53, 906-918. https://doi.org/10.1016/j.insmatheco.2013.10.003 |
| [6] | Bayraktar, E., Kyprianou, A. and Yamazaki, K. (2013) On Optimal Dividends in the Dual Model. Astin Bulletin, 43, 359-372. https://doi.org/10.1017/asb.2013.17 |
| [7] | Bayraktar, E., Kyprianou, A. and Yamazaki, K. (2013) Optimal Dividends in the Dual Model under Transaction Costs. arXiv:1301.7525v2 [math.PR] https://doi.org/10.1016/j.insmatheco.2013.11.007 |
| [8] | Albrecher, H., B？uerle, N. and Bladt, M. (2018) Dividends: From Refracting to Ratcheting. Insurance: Mathematics and Economics, 83, 47-58. https://doi.org/10.1016/j.insmatheco.2018.09.003 |
| [9] | Landriault, D., Li, B. and Lkabous, M.A. (2020) On Occupation Times in the Red of Lévy Risk Models. Insurance: Mathematics and Economics, 92, 17-26. https://doi.org/10.1016/j.insmatheco.2020.02.011 |
| [10] | Avanzi, B., Lau, H. and Wong, B. (2020) Optimal Periodic Dividend Strategies for Spectrally Positive Lévy Risk Processes with Fixed Transaction Costs. Insurance: Mathematics and Economics, 93, 315-332.
https://doi.org/10.1016/j.insmatheco.2020.05.012 |
| [11] | Kuznetsov, A., Kyprianou, A.E. and Rivero, V. (2013) The Theory of Scale Functions for Spectrally Negative Lévy Processes. Springer Verlag, Berlin Heidelberg. https://doi.org/10.1007/978-3-642-31407-0_2 |
| [12] | Yin, C.C. and Wen, Y.Z. (2013) Optimal Dividend Problem with a Terminal Value for Spectrally Positive Lévy Processes. Insurance: Mathematics and Economics, 53, 769-773. https://doi.org/10.1016/j.insmatheco.2013.09.019 |
| [13] | Yin, C.C., Wen, Y.Z. and Zhao, Y.X. (2014) On the Optimal Dividend Problem for a Spectrally Positive Lévy Processes. Astin Bulletin, 44, 635-651. https://doi.org/10.1017/asb.2014.12 |
