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随机利率下带注资的对偶模型最优分红问题

邓丽 郑华 彭小飞

邓丽, 郑华, 彭小飞. 随机利率下带注资的对偶模型最优分红问题[J]. 华南师范大学学报(自然科学版), 2020, 52(2): 107-113. doi: 10.6054/j.jscnun.2020033
引用本文: 邓丽, 郑华, 彭小飞. 随机利率下带注资的对偶模型最优分红问题[J]. 华南师范大学学报(自然科学版), 2020, 52(2): 107-113. doi: 10.6054/j.jscnun.2020033
DENG Li, ZHENG Hua, PENG Xiaofei. The Optimal Dividend Problem in Dual Model with Capital Injections by Stochastic Interest Rates[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(2): 107-113. doi: 10.6054/j.jscnun.2020033
Citation: DENG Li, ZHENG Hua, PENG Xiaofei. The Optimal Dividend Problem in Dual Model with Capital Injections by Stochastic Interest Rates[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(2): 107-113. doi: 10.6054/j.jscnun.2020033

随机利率下带注资的对偶模型最优分红问题

doi: 10.6054/j.jscnun.2020033
基金项目: 

国家自然科学基金项目 11801097

广东省基础研究及应用研究重点项目 2018KZDXM065

广东省自然科学基金项目 2018A0303130274

韶关学院科研项目 SY2016KJ18

详细信息
    通讯作者:

    郑华, 副教授, Email:hzhengjlfdu@gmail.com

  • 中图分类号: O211.6

The Optimal Dividend Problem in Dual Model with Capital Injections by Stochastic Interest Rates

  • 摘要: 在红利有界的条件下, 讨论了复合二项对偶模型中带比例交易费再注资且分红贴现利率随机变化的最优分红问题; 运用压缩映射不动点原理证明了该最优分红问题的最优值函数是一个离散的HJB方程的唯一解, 得到了最优分红策略和最优值函数的计算方法; 根据分红策略的一些性质, 得到了该最优值函数的可无限逼近的上界和下界,并采用了Bellman递归算法得到最优值函数和最优分红策略的数值解,从而得到最优分红算法.数值实例结果表明:该最优分红策略是有效的.这为公司的决策者在兼顾公司正常运营和股东利益而进行红利决策时提供了理论依据.
  • 表  1  最优分红策略φi*(u) (i=1, 2, 3, C=5)

    Table  1.   The optimal dividend strategy φi*(u) (i=1, 2, 3, C=5)

    u β=0 β=0.2 β=0.4 β=0.6 β=1.2 不注资
    i=1 i=2 i=3 i=1 i=2 i=3 i=1 i=2 i=3 i=1 i=2 i=3 i=1 i=2 i=3 i=1 i=2 i=3
    0, 1, …, 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    11 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
    12 2 2 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0
    13 3 3 3 3 3 3 2 1 1 0 0 0 0 0 0 0 0 0
    14 4 4 4 4 4 4 3 2 2 0 0 0 0 0 0 0 0 0
    15 5 5 5 5 5 5 4 3 3 0 0 0 0 0 0 0 0 0
    16 5 5 5 5 5 5 5 4 4 1 1 1 0 0 0 0 0 0
    17 5 5 5 5 5 5 5 5 5 2 2 2 0 0 0 0 0 0
    18 5 5 5 5 5 5 5 5 5 3 3 3 0 0 0 0 0 0
    19 5 5 5 5 5 5 5 5 5 4 4 4 0 0 0 0 0 0
    20 5 5 5 5 5 5 5 5 5 5 5 5 0 0 0 0 0 0
    21 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1
    22 5 5 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2
    23 5 5 5 5 5 5 5 5 5 5 5 5 3 3 3 3 3 3
    24 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4
    25, 26, … 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
    下载: 导出CSV

    表  2  最优值函数

    Table  2.   The optimal value function

    u β=0 β=0.2 β=1.2 不注资
    V1*(u) V2*(u) V3*(u) V1*(u) V2*(u) V3*(u) V1*(u) V2*(u) V3*(u) W1*(u) W2*(u) W3*(u)
    0 34.650 1 35.061 4 35.033 0 29.566 9 29.938 8 29.912 0 8.898 5 9.126 3 9.102 4 10.566 7 10.673 5 10.667 2
    1 35.650 1 36.061 4 36.033 0 30.766 9 31.138 8 31.112 0 11.098 5 11.326 3 11.302 4 11.740 8 11.859 4 11.852 5
    2 36.650 1 37.061 4 37.033 0 31.966 9 32.338 8 32.312 0 13.298 5 13.526 3 13.502 4 13.045 4 13.177 2 13.169 4
    3 37.650 1 38.061 4 38.033 0 33.166 9 33.538 8 33.512 0 15.498 5 15.726 3 15.702 4 14.494 9 14.641 3 14.632 7
    4 38.650 1 39.061 4 39.033 0 34.366 9 34.738 8 34.712 0 17.698 5 17.926 3 17.902 4 16.105 4 16.268 1 16.258 5
    5 39.650 1 40.061 4 40.033 0 35.566 9 35.938 8 35.912 0 19.898 5 20.126 3 20.102 4 20.153 1 20.357 0 20.344 9
    6 40.563 5 40.981 1 40.953 3 36.611 9 36.990 9 36.964 8 21.621 3 21.861 2 21.838 3 21.514 1 21.731 7 21.718 8
    7 41.471 9 41.896 0 41.868 7 37.645 3 38.031 5 38.006 1 23.301 5 23.553 2 23.531 4 22.928 8 23.160 6 23.146 9
    8 42.374 9 42.805 5 42.778 7 38.665 7 39.059 2 39.034 4 24.934 2 25.197 8 25.176 8 24.392 3 24.638 7 24.624 2
    9 43.271 8 43.708 9 43.682 6 39.671 9 40.072 7 40.048 5 26.514 1 26.789 7 26.769 4 25.897 9 26.159 4 26.144 0
    10 44.161 9 44.605 7 44.579 8 40.662 1 41.070 4 41.046 6 28.035 4 28.322 8 28.303 1 27.919 5 28.201 3 28.184 9
    11 45.026 6 45.477 8 45.452 1 41.602 2 42.018 6 41.995 0 29.391 2 29.691 0 29.671 3 29.159 1 29.453 2 29.436 1
    12 45.888 8 46.347 3 46.321 8 42.532 9 42.957 1 42.933 7 30.704 5 31.016 4 30.996 6 30.402 4 30.708 8 30.691 0
    13 46.748 7 47.214 4 47.189 1 43.453 8 43.885 9 43.862 6 31.974 3 32.298 0 32.278 1 31.643 1 31.961 7 31.943 4
    14 47.606 4 48.079 3 48.054 2 44.365 1 44.804 8 44.781 8 33.199 6 33.534 7 33.514 7 32.874 3 33.204 9 33.186 1
    15 48.462 3 48.942 3 48.917 3 45.266 9 45.714 1 45.691 2 34.380 0 34.726 1 34.705 8 34.191 7 34.535 2 34.515 8
    16 49.341 0 49.827 5 49.802 9 46.164 5 46.618 4 46.596 0 35.493 8 35.850 4 35.829 9 35.272 3 35.626 3 35.606 4
    17 50.210 9 50.704 0 50.679 8 47.055 5 47.516 2 47.494 1 36.577 4 36.944 3 36.923 6 36.341 4 36.705 5 36.685 3
    18 51.071 1 51.570 8 51.546 9 47.939 0 48.406 6 48.384 8 37.631 9 38.008 7 37.987 7 37.395 8 37.770 0 37.749 4
    19 51.920 3 52.426 9 52.403 2 48.814 2 49.289 0 49.267 4 38.658 4 39.044 8 39.023 6 38.432 8 38.816 7 38.795 8
    20 52.757 5 53.271 1 53.247 6 49.680 3 50.162 3 50.140 8 39.658 4 40.054 0 40.032 6 39.471 9 39.865 5 39.844 3
    21 53.553 2 54.074 4 54.050 7 50.524 1 51.014 3 50.992 6 40.629 3 41.033 7 41.012 2 40.435 0 40.837 4 40.816 1
    22 54.344 3 54.873 2 54.849 3 51.359 2 51.857 5 51.835 6 41.582 6 41.995 6 41.974 0 41.387 3 41.798 3 41.776 8
    23 55.130 8 55.667 3 55.643 1 52.185 7 52.692 0 52.669 8 42.519 7 42.941 1 42.919 4 42.328 0 42.747 4 42.725 8
    24 55.912 3 56.456 4 56.432 0 53.003 5 53.517 7 53.495 4 43.442 4 43.871 9 43.850 2 43.256 8 43.684 4 43.662 8
    25 56.688 7 57.240 3 57.215 7 53.812 9 54.335 0 54.312 3 44.352 3 44.789 6 44.767 9 44.178 5 44.614 0 44.592 5
    26 57.464 8 58.023 8 57.999 1 54.614 9 55.144 7 55.121 9 45.255 6 45.699 7 45.678 4 45.082 5 45.524 8 45.503 6
    27 58.231 4 58.797 9 58.772 9 55.408 8 55.946 3 55.923 3 46.152 9 46.603 9 46.582 9 45.980 5 46.429 6 46.408 8
    28 58.988 2 59.562 1 59.536 9 56.194 2 56.739 4 56.716 1 47.043 5 47.501 4 47.480 7 46.871 8 47.328 0 47.307 4
    29 59.735 0 60.316 3 60.290 7 56.970 8 57.523 7 57.500 0 47.926 5 48.391 7 48.371 1 47.755 7 48.219 2 48.198 7
    30 60.471 5 61.060 1 61.034 2 57.738 3 58.298 8 58.274 8 48.801 3 49.273 9 49.253 4 48.631 4 49.102 3 49.081 9
    下载: 导出CSV
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  • 收稿日期:  2019-09-19
  • 刊出日期:  2020-04-25

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