On a risk model with randomized dividend-decision times.

*(English)*Zbl 1282.91164Summary: In this paper, we consider a perturbed compound Poisson risk model with a randomized dividend strategy. Assume that decisions on paying off dividends are made at some random observation times. Whenever the observed value of the surplus process exceeds a given barrier \(b\), the excess value will be paid off as dividends. We assume that the Laplace transform of the individual claim size belongs to the rational family. When the time intervals between successive decision times follow exponential distribution, we present explicit expressions for the Gerber-Shiu function. We also extend the exponential assumption to Erlang and discuss the solution procedure.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

91G50 | Corporate finance (dividends, real options, etc.) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

##### Keywords:

perturbed compound Poisson risk model; dividend-decision time; Gerber-Shiu function; integral equation; exponential; Erlang
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\textit{Z. Zhang}, J. Ind. Manag. Optim. 10, No. 4, 1041--1058 (2014; Zbl 1282.91164)

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##### References:

[1] | H. Albrecher, Randomized observation periods for the compound Poisson risk model: Dividends,, Astin Bulletin, 41, 645, (2011) · Zbl 1239.91072 |

[2] | H. Albrecher, Randomized observation periods for the compound Poisson risk model: The discounted penalty function,, Scandinavian Actuarial Journal, 2013, 424, (2013) · Zbl 1401.91089 |

[3] | B. Avanzi, On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency,, Insurance: Mathematics and Economics, 52, 98, (2013) · Zbl 1291.91088 |

[4] | B. De Finetti, Su un impostazione alternativa della teoria collectiva del rischio,, Transactions of the XVth International Congress of Actuaries, 2, 433, (1957) |

[5] | H. U. Gerber, On the time value of ruin,, North American Actuarial Journal, 2, 48, (1998) · Zbl 1081.60550 |

[6] | H. U. Gerber, Optimal dividends: Analysis with Brownian motion,, North American Actuarial Journal, 8, 1, (2004) · Zbl 1085.62122 |

[7] | A. E. Kyprianou, <em>Introductory Lectures on Fluctuations of Lévy Processes with Applications</em>,, Springer-Verlag, (2006) · Zbl 1104.60001 |

[8] | S. Li, The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion,, Scandinavian Actuarial Journal, 2006, 73, (2006) · Zbl 1143.91032 |

[9] | S. Li, On ruin for the Erlang(n) risk model,, Insurance: Mathematics and Economics, 34, 391, (2004) · Zbl 1188.91089 |

[10] | S. Li, On a class of renewal risk model with a constant dividend barrier,, Insurance: Mathematics and Economics, 35, 691, (2004) · Zbl 1122.91345 |

[11] | X. S. Lin, The classical risk model with a constant dividend barrier: Analysis of the Gerber-Shiu discounted penalty function,, Insurance: Mathematics and Economics, 33, 551, (2003) · Zbl 1103.91369 |

[12] | X. S. Lin, The compound Poisson risk model with a threshold dividend strategy,, Insurance: Mathematics and Economics, 38, 57, (2006) · Zbl 1157.91383 |

[13] | X. S. Lin, The compound Poisson risk model with multiple thresholds,, Insurance: Mathematics and Economics, 42, 617, (2008) · Zbl 1152.91592 |

[14] | C. C. L. Tsai, A generalized defective renewal equation for the surplus process perturbed by diffusion,, Insurance: Mathematics and Economics, 30, 51, (2002) · Zbl 1074.91563 |

[15] | Z. Zhang, Dividend payments in the Brownian risk model with randomized decision times,, Acta Mathematicae Applicatae Sinica-English Series, (2013) |

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