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The threshold dividend strategy on a class of dual model with tax payments

  • 1.

    College of Sciences, Jiangxi Agricultural University, Nanchang 330045, China

  • 2.

    School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Funds:  Supposed by the Fundamental Research Funds for the Central Universities of China and Jiangxi Agricultural University Youth Science Foundation (09003326).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.03.003
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  • Author Bio:

    LIU Zhang, male, born in 1981, master/leture. Research field: Financial and actuarial mathematics.

  • Corresponding author: WANG Wenyuan
  • Received Date: 07 September 2012
  • Accepted Date: 24 February 2013
  • Rev Recd Date: 24 February 2013
  • Publish Date: 30 March 2014
    Abstract

  • Abstract

    A class of dual risk model was considered in which dividends are paid under a threshold strategy and tax payments are paid according to a loss-carry forward system. For this model, the expectation of the discounted dividends until ruin was investigated and their corresponding integral equations, integro-differential equations and analytical expressions were derived. Finally, the case where profits follow an Erlang(2) distribution was solved.

    Abstract

    A class of dual risk model was considered in which dividends are paid under a threshold strategy and tax payments are paid according to a loss-carry forward system. For this model, the expectation of the discounted dividends until ruin was investigated and their corresponding integral equations, integro-differential equations and analytical expressions were derived. Finally, the case where profits follow an Erlang(2) distribution was solved.
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    • References(20)
  • [1]
    Avanzi B, Gerber H U, Shiu E S W. Optimal dividends in the dual model [J]. Insurance: Mathematics and Economics, 2007,41:111-123.
    [2]
    Avanzi B, Gerber H U. Optimal dividends in the dual model with diffusion [J]. ASTIN Bulletin, 2008,38(2):653667.
    [3]
    Avanzi B, Shen J, Wong B. Optimal dividends and capital injections in the dual model with diffusion [J]. ASTIN Bulletin, 2011,41(2):611-644.
    [4]
    Gerber H, Smith N. Optimal dividends with incomplete information in the dual model [J]. Insurance: Mathematics and Economics, 2008,43(2):227-233.
    [5]
    Ng Andrew C Y. On a dual model with a dividend threshold[J]. Insurance: Mathematics and Economics, 2009, 44(2): 315-324.
    [6]
    Liu Z, Ming R X, Wang W Y, et al. The threshold dividend strategy in the dual risk model perturbed by diffusion[J]．Journal of University of Science and Technology of China, 2012, 42(6): 475-481.
    [7]
    Albrecher H, Badescu A, Landriault D. On the dual risk model with tax payments[J]. Insurance: Mathematics and Economics, 2008, 42: 1 086-1 094.
    [8]
    Albrecher H, Borst S, Boxma O, et al. The tax identity in risk theory: A simple proof and an extension[J]. Insurance: Mathematics and Economics, 2009, 44: 304-306.
    [9]
    Albrecher H, Hipp C. Lundbergs risk process with tax[J]. Bltter der DGVFM, 2007, 28(1): 13-28.
    [10]
    Albrecher H, Renaud J, Zhou X W. A lévy insurance risk process with tax[J]. Journal of Applied Probability, 2008, 45: 363-375.
    [11]
    Wei L. Ruin probability in the presence of interest earnings and tax payments[J]. Insurance: Mathematics and Economics, 2009, 45: 133-138.
    [12]
    Ming R X, Wang W Y, Xiao L Q. On the time value of absolute ruin with tax[J]. Insurance: Mathematics and Economics, 2010, 46(1): 67-84.
    [13]
    Wang W Y, Ming R X, Hu Y J. On the expected discounted penalty function for the risk process with tax[J]. Statistics and Probability Letters, 2011, 81(4): 489-501.
    [14]
    Wang W Y, Hu Y J. Optimal loss-carry-forward taxation for the levy risk model[J]. Insurance: Mathematics and Economics, 2012, 50(1): 121-130.
    [15]
    Liu Z, Zhang A L, Li C H. The expected discounted tax payments on dual risk model under a dividend threshold[J]．Open Journal of Statistics, 2013, 3: 136-144.
    [16]
    Gerber H U, Shiu E S W. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10(2): 76-93.
    [17]
    De Finetti B. Su unimpostazione alternativa della teoria collettiva del rischio[C]// Proceedings of the Transactions of the XV International Congress of Actuaries, 1957, 2: 433-443.
    [18]
    Dong Y, Wang G, Yuen K C. On the renewal risk model under a threshold strategy[J]. Journal of Computational and Applied Mathematics, 2009, 230(1): 22-33.
    [19]
    Gerber H U, Shiu E S W. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin[J]. Insurance: Mathematics and Economics, 1997, 21: 129-137.
    [20]
    Gerber H U, Shiu E S W. On the time value of ruin[J]. North American Actuarial Journal, 1998, 2: 48-78.
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    [1]
    Avanzi B, Gerber H U, Shiu E S W. Optimal dividends in the dual model [J]. Insurance: Mathematics and Economics, 2007,41:111-123.
    [2]
    Avanzi B, Gerber H U. Optimal dividends in the dual model with diffusion [J]. ASTIN Bulletin, 2008,38(2):653667.
    [3]
    Avanzi B, Shen J, Wong B. Optimal dividends and capital injections in the dual model with diffusion [J]. ASTIN Bulletin, 2011,41(2):611-644.
    [4]
    Gerber H, Smith N. Optimal dividends with incomplete information in the dual model [J]. Insurance: Mathematics and Economics, 2008,43(2):227-233.
    [5]
    Ng Andrew C Y. On a dual model with a dividend threshold[J]. Insurance: Mathematics and Economics, 2009, 44(2): 315-324.
    [6]
    Liu Z, Ming R X, Wang W Y, et al. The threshold dividend strategy in the dual risk model perturbed by diffusion[J]．Journal of University of Science and Technology of China, 2012, 42(6): 475-481.
    [7]
    Albrecher H, Badescu A, Landriault D. On the dual risk model with tax payments[J]. Insurance: Mathematics and Economics, 2008, 42: 1 086-1 094.
    [8]
    Albrecher H, Borst S, Boxma O, et al. The tax identity in risk theory: A simple proof and an extension[J]. Insurance: Mathematics and Economics, 2009, 44: 304-306.
    [9]
    Albrecher H, Hipp C. Lundbergs risk process with tax[J]. Bltter der DGVFM, 2007, 28(1): 13-28.
    [10]
    Albrecher H, Renaud J, Zhou X W. A lévy insurance risk process with tax[J]. Journal of Applied Probability, 2008, 45: 363-375.
    [11]
    Wei L. Ruin probability in the presence of interest earnings and tax payments[J]. Insurance: Mathematics and Economics, 2009, 45: 133-138.
    [12]
    Ming R X, Wang W Y, Xiao L Q. On the time value of absolute ruin with tax[J]. Insurance: Mathematics and Economics, 2010, 46(1): 67-84.
    [13]
    Wang W Y, Ming R X, Hu Y J. On the expected discounted penalty function for the risk process with tax[J]. Statistics and Probability Letters, 2011, 81(4): 489-501.
    [14]
    Wang W Y, Hu Y J. Optimal loss-carry-forward taxation for the levy risk model[J]. Insurance: Mathematics and Economics, 2012, 50(1): 121-130.
    [15]
    Liu Z, Zhang A L, Li C H. The expected discounted tax payments on dual risk model under a dividend threshold[J]．Open Journal of Statistics, 2013, 3: 136-144.
    [16]
    Gerber H U, Shiu E S W. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10(2): 76-93.
    [17]
    De Finetti B. Su unimpostazione alternativa della teoria collettiva del rischio[C]// Proceedings of the Transactions of the XV International Congress of Actuaries, 1957, 2: 433-443.
    [18]
    Dong Y, Wang G, Yuen K C. On the renewal risk model under a threshold strategy[J]. Journal of Computational and Applied Mathematics, 2009, 230(1): 22-33.
    [19]
    Gerber H U, Shiu E S W. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin[J]. Insurance: Mathematics and Economics, 1997, 21: 129-137.
    [20]
    Gerber H U, Shiu E S W. On the time value of ruin[J]. North American Actuarial Journal, 1998, 2: 48-78.
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