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        帶隨機回報的一類離散馬氏風險模型的分紅問題(英文)

        2014-11-14 16:06:44鄧迎春樂勝杰肖和錄

        鄧迎春 樂勝杰 肖和錄 等

        摘要考慮了帶隨機回報的一類離散馬氏風險模型.在此模型中,賠付的發(fā)生概率,賠付額的分布函數(shù)都是由一個離散時間的馬氏鏈調(diào)控.當保險公司采用門檻分紅策略時,通過計算得到了破產(chǎn)前的期望折現(xiàn)分紅總量滿足的一組線性方程.最后,給出了期望折現(xiàn)分紅總量的顯式解析式.

        關(guān)鍵詞馬氏風險模型;隨機回報;門檻分紅;期望折現(xiàn)分紅量

        We introduce a constant dividend barrier into the model (1). Assume that any surplus of the insurer above the level b (a positive integer) is immediately paid out to the shareholders so that the surplus is brought back to the level b. When the surplus is below, nothing is done. Once the surplus is negative, the insurer is ruined and the process stops. Let V(n) denote the surplus at time n. Then

        References:

        [1]YUEN K C, GUO J. Ruin probabilities for timecorrelated claims in the compound binomial model[J].Insurance: Math Eco, 2001,29(1):4757.

        [2]GERBER H U. Mathematical fun with the compound binomial process[J]. Astin Bull, 1988,18(2):161168.

        [3]CHENG S, GERBER H U, SHIU E S W. Discounted pribabilities and ruin theory in the compound binomial model[J]. Insurance: Math Eco, 2000,26(23):239250.

        [4]GONG R, YANG X. The nite time survival probabilities in the fully discrete compound binomial model[J]. Chin J Appl Probab Statist, 2001,17(4):6599.

        [5]TAN J Y, YANG X Q. The divideng problems for compound binomoal model with stochastic return on investments[J]. Nonlinear Math for Uncertainty Appl, 2011,100:239246.

        [6]TAN J Y, YANG X Q. The compound binomial model with randomized decisions on paying dividends[J]. Insurance: Math Eco, 2006,39(1):118.

        [7]DE FINETTI B. Su unimpostazione alternativa della teoria collettiva del rischio[J]. Transactions of the XVth International Congress of Actuaries, 1957,2:433443.

        [8]LIN X S, WILLMOT G E, DREKIC S. The classical risk model with a constant dividend barrier:Analysis of the GerberShiu discounted penalty function[J]. Insurance: Math Eco, 2003,33(3):551566.

        [9]LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy[J].Insurance: Math Eco, 2006,38(1):5780.

        [10]ZHOU J M, OU H, MO X Y, et al. The compound Poisson risk model perturbed by diusion with doublethreshold dividend barriers to shareholders and policyholders[J]. J Natur Sci Hunan Norm Univ, 2012,35(6):113.

        [11]COSSETTE H, LANDRIAULT D, MARCEAN E. Compound binomial risk model in a Markovian environment[J]. Insurance: Math Eco, 2004,35(2):425443.

        [12]YUEN K C, GUO J Y. Some results on the compound Markov binomial model[J]. Scand Actuar J, 2006,2006(3):129140.

        [13]PAULSEN J, GJESSING H K. Optimal choice of dividend barriers for a risk process with stochastic return on investments[J]. Insurance: Math Eco, 1997,20(3):215223.

        (編輯胡文杰)

        摘要考慮了帶隨機回報的一類離散馬氏風險模型.在此模型中,賠付的發(fā)生概率,賠付額的分布函數(shù)都是由一個離散時間的馬氏鏈調(diào)控.當保險公司采用門檻分紅策略時,通過計算得到了破產(chǎn)前的期望折現(xiàn)分紅總量滿足的一組線性方程.最后,給出了期望折現(xiàn)分紅總量的顯式解析式.

        關(guān)鍵詞馬氏風險模型;隨機回報;門檻分紅;期望折現(xiàn)分紅量

        We introduce a constant dividend barrier into the model (1). Assume that any surplus of the insurer above the level b (a positive integer) is immediately paid out to the shareholders so that the surplus is brought back to the level b. When the surplus is below, nothing is done. Once the surplus is negative, the insurer is ruined and the process stops. Let V(n) denote the surplus at time n. Then

        References:

        [1]YUEN K C, GUO J. Ruin probabilities for timecorrelated claims in the compound binomial model[J].Insurance: Math Eco, 2001,29(1):4757.

        [2]GERBER H U. Mathematical fun with the compound binomial process[J]. Astin Bull, 1988,18(2):161168.

        [3]CHENG S, GERBER H U, SHIU E S W. Discounted pribabilities and ruin theory in the compound binomial model[J]. Insurance: Math Eco, 2000,26(23):239250.

        [4]GONG R, YANG X. The nite time survival probabilities in the fully discrete compound binomial model[J]. Chin J Appl Probab Statist, 2001,17(4):6599.

        [5]TAN J Y, YANG X Q. The divideng problems for compound binomoal model with stochastic return on investments[J]. Nonlinear Math for Uncertainty Appl, 2011,100:239246.

        [6]TAN J Y, YANG X Q. The compound binomial model with randomized decisions on paying dividends[J]. Insurance: Math Eco, 2006,39(1):118.

        [7]DE FINETTI B. Su unimpostazione alternativa della teoria collettiva del rischio[J]. Transactions of the XVth International Congress of Actuaries, 1957,2:433443.

        [8]LIN X S, WILLMOT G E, DREKIC S. The classical risk model with a constant dividend barrier:Analysis of the GerberShiu discounted penalty function[J]. Insurance: Math Eco, 2003,33(3):551566.

        [9]LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy[J].Insurance: Math Eco, 2006,38(1):5780.

        [10]ZHOU J M, OU H, MO X Y, et al. The compound Poisson risk model perturbed by diusion with doublethreshold dividend barriers to shareholders and policyholders[J]. J Natur Sci Hunan Norm Univ, 2012,35(6):113.

        [11]COSSETTE H, LANDRIAULT D, MARCEAN E. Compound binomial risk model in a Markovian environment[J]. Insurance: Math Eco, 2004,35(2):425443.

        [12]YUEN K C, GUO J Y. Some results on the compound Markov binomial model[J]. Scand Actuar J, 2006,2006(3):129140.

        [13]PAULSEN J, GJESSING H K. Optimal choice of dividend barriers for a risk process with stochastic return on investments[J]. Insurance: Math Eco, 1997,20(3):215223.

        (編輯胡文杰)

        摘要考慮了帶隨機回報的一類離散馬氏風險模型.在此模型中,賠付的發(fā)生概率,賠付額的分布函數(shù)都是由一個離散時間的馬氏鏈調(diào)控.當保險公司采用門檻分紅策略時,通過計算得到了破產(chǎn)前的期望折現(xiàn)分紅總量滿足的一組線性方程.最后,給出了期望折現(xiàn)分紅總量的顯式解析式.

        關(guān)鍵詞馬氏風險模型;隨機回報;門檻分紅;期望折現(xiàn)分紅量

        We introduce a constant dividend barrier into the model (1). Assume that any surplus of the insurer above the level b (a positive integer) is immediately paid out to the shareholders so that the surplus is brought back to the level b. When the surplus is below, nothing is done. Once the surplus is negative, the insurer is ruined and the process stops. Let V(n) denote the surplus at time n. Then

        References:

        [1]YUEN K C, GUO J. Ruin probabilities for timecorrelated claims in the compound binomial model[J].Insurance: Math Eco, 2001,29(1):4757.

        [2]GERBER H U. Mathematical fun with the compound binomial process[J]. Astin Bull, 1988,18(2):161168.

        [3]CHENG S, GERBER H U, SHIU E S W. Discounted pribabilities and ruin theory in the compound binomial model[J]. Insurance: Math Eco, 2000,26(23):239250.

        [4]GONG R, YANG X. The nite time survival probabilities in the fully discrete compound binomial model[J]. Chin J Appl Probab Statist, 2001,17(4):6599.

        [5]TAN J Y, YANG X Q. The divideng problems for compound binomoal model with stochastic return on investments[J]. Nonlinear Math for Uncertainty Appl, 2011,100:239246.

        [6]TAN J Y, YANG X Q. The compound binomial model with randomized decisions on paying dividends[J]. Insurance: Math Eco, 2006,39(1):118.

        [7]DE FINETTI B. Su unimpostazione alternativa della teoria collettiva del rischio[J]. Transactions of the XVth International Congress of Actuaries, 1957,2:433443.

        [8]LIN X S, WILLMOT G E, DREKIC S. The classical risk model with a constant dividend barrier:Analysis of the GerberShiu discounted penalty function[J]. Insurance: Math Eco, 2003,33(3):551566.

        [9]LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy[J].Insurance: Math Eco, 2006,38(1):5780.

        [10]ZHOU J M, OU H, MO X Y, et al. The compound Poisson risk model perturbed by diusion with doublethreshold dividend barriers to shareholders and policyholders[J]. J Natur Sci Hunan Norm Univ, 2012,35(6):113.

        [11]COSSETTE H, LANDRIAULT D, MARCEAN E. Compound binomial risk model in a Markovian environment[J]. Insurance: Math Eco, 2004,35(2):425443.

        [12]YUEN K C, GUO J Y. Some results on the compound Markov binomial model[J]. Scand Actuar J, 2006,2006(3):129140.

        [13]PAULSEN J, GJESSING H K. Optimal choice of dividend barriers for a risk process with stochastic return on investments[J]. Insurance: Math Eco, 1997,20(3):215223.

        (編輯胡文杰)

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