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The threshold dividends in the Cramr-Lundberg risk model with loss-carry forward tax payments

Funds:  Supported by the National Natural Science Foundation of China (11771343, 11601097) and the Science and Technology Research Project of Jiangxi Provincial Education Department (GJJ180201,GJJ150401).
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https://doi.org/10.3969/j.issn.0253-2778.2018.11.002
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  • Corresponding author: LIU Zhang (corresponding author), male, born in 1981, PhD/lecturer. Research field: Financial and actuarial mathematics. E-mail: liuzhang1006@163.com
  • Received Date: 20 December 2017
  • Accepted Date: 07 May 2018
  • Rev Recd Date: 07 May 2018
  • Publish Date: 30 November 2018
    Abstract

  • Abstract

    A classical Cramr-Lundberg risk model with a threshold dividend strategy and loss-carry forward tax payments was studied. For this model, the closed-form expressions for the expected accumulated discounted dividends until ultimate ruin was derived and the explicit solution was presented when the individual claim amount follows an exponential distribution. Finally, numerical

    Abstract

    A classical Cramr-Lundberg risk model with a threshold dividend strategy and loss-carry forward tax payments was studied. For this model, the closed-form expressions for the expected accumulated discounted dividends until ultimate ruin was derived and the explicit solution was presented when the individual claim amount follows an exponential distribution. Finally, numerical
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    • References(21)
  • [1]
    DE FINETTI B. Su un’impostazione alternativa della teoria collettiva del rischio[C]// Proceedings of the Transactions of the XVth International Congress of Actuaries. London: Institute of Actuaries Students’ Society, 1957, 2: 433-443.
    [2]
    ASMUSSEN S, TAKSAR M. Controlled diffusion models for optimal dividend pay-out[J]. Insurance: Mathematics and Economics, 1997, 20(1): 1-15.
    [3]
    GERBER H, SHIU E. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10: 76-93.
    [4]
    GERBER H, SHIU E. On the time value of ruin[J]. North American Actuarial Journal, 1998, 2: 48-78.
    [5]
    DICKSON D C M, WATERS H R. Some optimal dividend problems[J]. ASTIN Bulletin, 2004, 34: 49-74.
    [6]
    ALBRECHER H, HARTINGER J, TICHY R. On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier[J]. Scandinavian Actuarial Journal, 2005（2）: 103-126.
    [7]
    LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy[J]. Insurance: Mathematics and Economics, 2005, 38: 57-80.
    [8]
    AVANZI B. Strategies for dividend distribution: A review[J]. North American Actuarial Journal, 2009, 13(2): 217-251.
    [9]
    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.
    [10]
    CHEUNG E C K, LIU H, WOO J K. On the joint analysis of the total discounted payments to policyholders and shareholders: Dividend barrier strategy[J]. Risks, 2015, 3(4): 491-514.
    [11]
    ALBRECHER H, HIPP C. Lundberg’s risk process with tax[J]. Bltter der DGVFM, 2007, 28(1): 13-28.
    [12]
    ALBRECHER H, BADESCU A, LANDRIAULT D. On the dual risk model with taxation[J]. Insurance: Mathematics and Economics, 2008, 42: 1086-1094.
    [13]
    KYPRIANOU A, ZHOU X W. General tax structures and the Lévy insurance risk model[J]. Journal of Applied Probability, 2009, 46: 1146-1156.
    [14]
    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.
    [15]
    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: 67-84.
    [16]
    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: 489-501.
    [17]
    AVRAM F, VU N L, ZHOU X. On taxed spectrally negative Lévy processes with draw-down stopping[J]. Insurance: Mathematics and Economics, 2017, 76: 69-74.
    [18]
    LIU Z, WANG W Y. The threshold dividend strategy on a class of dual model with tax payments[J]. Journal of University of Science and Technology of China, 2014, 44(3): 181-187.
    [19]
    WANG W Y, XIAO L, MING R X, et al. On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy[J]. Applied Mathematics: A Journal of Chinese Universities, 2013, 28(1): 27-39.
    [20]
    WANG W Y, LIU Z. The expected discounted penalty function under the compound Poisson risk model with tax payments and a threshold dividend strategy[J]. Journal of University of Science and Technology of China, 2016, 46(2): 87-94.
    [21]
    ALBRECHER H, RENAUD J, ZHOU X W. A Lévy insurance risk process with tax[J]. Journal of Applied Probability, 2008, 45: 363-375.)
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    [1]
    DE FINETTI B. Su un’impostazione alternativa della teoria collettiva del rischio[C]// Proceedings of the Transactions of the XVth International Congress of Actuaries. London: Institute of Actuaries Students’ Society, 1957, 2: 433-443.
    [2]
    ASMUSSEN S, TAKSAR M. Controlled diffusion models for optimal dividend pay-out[J]. Insurance: Mathematics and Economics, 1997, 20(1): 1-15.
    [3]
    GERBER H, SHIU E. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10: 76-93.
    [4]
    GERBER H, SHIU E. On the time value of ruin[J]. North American Actuarial Journal, 1998, 2: 48-78.
    [5]
    DICKSON D C M, WATERS H R. Some optimal dividend problems[J]. ASTIN Bulletin, 2004, 34: 49-74.
    [6]
    ALBRECHER H, HARTINGER J, TICHY R. On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier[J]. Scandinavian Actuarial Journal, 2005（2）: 103-126.
    [7]
    LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy[J]. Insurance: Mathematics and Economics, 2005, 38: 57-80.
    [8]
    AVANZI B. Strategies for dividend distribution: A review[J]. North American Actuarial Journal, 2009, 13(2): 217-251.
    [9]
    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.
    [10]
    CHEUNG E C K, LIU H, WOO J K. On the joint analysis of the total discounted payments to policyholders and shareholders: Dividend barrier strategy[J]. Risks, 2015, 3(4): 491-514.
    [11]
    ALBRECHER H, HIPP C. Lundberg’s risk process with tax[J]. Bltter der DGVFM, 2007, 28(1): 13-28.
    [12]
    ALBRECHER H, BADESCU A, LANDRIAULT D. On the dual risk model with taxation[J]. Insurance: Mathematics and Economics, 2008, 42: 1086-1094.
    [13]
    KYPRIANOU A, ZHOU X W. General tax structures and the Lévy insurance risk model[J]. Journal of Applied Probability, 2009, 46: 1146-1156.
    [14]
    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.
    [15]
    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: 67-84.
    [16]
    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: 489-501.
    [17]
    AVRAM F, VU N L, ZHOU X. On taxed spectrally negative Lévy processes with draw-down stopping[J]. Insurance: Mathematics and Economics, 2017, 76: 69-74.
    [18]
    LIU Z, WANG W Y. The threshold dividend strategy on a class of dual model with tax payments[J]. Journal of University of Science and Technology of China, 2014, 44(3): 181-187.
    [19]
    WANG W Y, XIAO L, MING R X, et al. On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy[J]. Applied Mathematics: A Journal of Chinese Universities, 2013, 28(1): 27-39.
    [20]
    WANG W Y, LIU Z. The expected discounted penalty function under the compound Poisson risk model with tax payments and a threshold dividend strategy[J]. Journal of University of Science and Technology of China, 2016, 46(2): 87-94.
    [21]
    ALBRECHER H, RENAUD J, ZHOU X W. A Lévy insurance risk process with tax[J]. Journal of Applied Probability, 2008, 45: 363-375.)
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