Some Results on a Double Compound Poisson-Geometric Risk Model with Interference ()

Dezhi Yan

Department of Economic, Shandong Jiaotong University, Jinan, China.

**DOI: **10.4236/tel.2012.21008
PDF HTML
5,730
Downloads
8,830
Views
Citations

Department of Economic, Shandong Jiaotong University, Jinan, China.

In this paper, we study the actual operating of an insurance company with random income. A double compound Poisson-Geometric risk model with interference was established. By using the martingale method, the adjustment coefficient equation, the formula and the upper bound of ruin probability, the time to reach a given level in this new risk mo- del were obtained.

Share and Cite:

D. Yan, "Some Results on a Double Compound Poisson-Geometric Risk Model with Interference," *Theoretical Economics Letters*, Vol. 2 No. 1, 2012, pp. 45-49. doi: 10.4236/tel.2012.21008.

Conflicts of Interest

The authors declare no conflicts of interest.

[1] | J. Grandell, “Aspects of Risk Theory,” Springer, Berlin, 1991. doi:10.1007/978-1-4613-9058-9 |

[2] | H. U. Gerber, “An Introduction to Mathematical Risk Theory,” Monograph Series, Vol. 8, S. S. Heubner Foundation, Philadelphia, 1979. |

[3] | F. Dufresne and H. U. Gerber, “Risk Theory for the Compound Poisson Process That Is Disturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 10, 1991, pp. 51-59. doi:10.1016/0167-6687(91)90023-Q |

[4] | N. Veraverbeke, “Asymptotic Estimations for the Probability of Ruin in a Pois-son Model with Diffusion,” Insurance: Mathematics and Economics, Vol. 13, 1993, pp. 57-62. doi:10.1016/0167-6687(93)90535-W |

[5] | H. U. Gerber and B. Landry, “On the Discounted Penalty at Ruin in a Jump-Diffusion and the Perturbed Put Option,” Insurance: Mathematics and Economics, Vol. 22, 1998, pp. 263-276. doi:10.1016/S0167-6687(98)00014-6 |

[6] | H. U. Gerber and E. S. W. Shiu, “On the Time Value of Ruin,” North American Actuarial Journal, Vol. 2, No. 1, 1998, pp. 48-78. |

[7] | G. J. Wang and R. Wu, “Some Distributions for Classic Risk Process That Is Perturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 26, No. 1, 2000, pp. 15-24. doi:10.1016/S0167-6687(99)00035-9 |

[8] | G. J. Wang, “A Decomposition of the Ruin Probability for the Risk Process Perturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 28, No. 1, 2001, pp. 49-59. doi:10.1016/S0167-6687(00)00065-2 |

[9] | C. C.-L. Tsai, “On the Discounted Distribution Functions of the Surplus Process,” Insurance: Mathematics and Economics, Vol. 28, No. 3, 2001, pp. 401-419. doi:10.1016/S0167-6687(01)00067-1 |

[10] | C. C.-L. Tsai, “A Generalized Defective Renewal Equation for the Surplus Process Perturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 30, No. 1, 2002, pp. 51-66. doi:10.1016/S0167-6687(01)00096-8 |

[11] | C. C.-L. Tsai, “On the Expectations of the Present Values of the Time of Ruin Perturbed by Diffusion,” Insurance: Mathematics and Eco-nomics, Vol. 32, No. 3, 2003, pp. 413-429. doi:10.1016/S0167-6687(03)00130-6 |

[12] | C. S. Zhang and G. J. Wang, “The Joint Density Function of Three Characteristics on Jump-Diffusion Risk Process,” Insurance: Mathematics and Economics, Vol. 32, No. 3, 2003, pp. 445-455. doi:10.1016/S0167-6687(03)00133-1 |

[13] | S. N. Chiu and C. C. Yin, “The Time of Ruin, the Surplus Prior to Ruin and the Deficit at Ruin for the Classical Process Perturbed by Diffusion,” Insurance: Mathematics and Economics, Vol. 33, No. 1, 2003, pp. 59-66. doi:10.1016/S0167-6687(03)00143-4 |

[14] | J. Paulsen, “Risk Theory in a Stochastic Environment,” Stochastic Process and Their Applications, Vol. 21, 1993, pp. 327-361. |

[15] | J. Paulsen, “Ruin Theory with Compounding Assets: A Survey,” Insurance: Mathematics and Economics, Vol. 22, No. 1, 1998, pp. 3-16. doi:10.1016/S0167-6687(98)00009-2 |

[16] | J. Paulsen and H. K. Gjessing, “Ruin Theory with Stochastic Return on Invest-ments,” Advances in Applied Probability, Vol. 29, 1997, pp. 965-985. doi:10.2307/1427849 |

[17] | V. Kalashnikov and R. Norberg, “Power Tailed Ruin Probabilities in the Presence of Risky Investments,” Stochastic Process and Their Applications, Vol. 98, 2002, pp. 221-228. |

[18] | V. E. Bening, V. Yu. Korolev and L. X. Liu, “Asymptotic Behavior of Generalized Risk Processes,” Acta Mathematica Sinica, English Series, Vol. 20, No. 2, 2004, pp. 349-356. doi:10.1007/s10114-003-0244-8 |

[19] | J. Cai, “Ruin Probability and Penalty Functions with Stochastic Rates of Interest,” Stochastic Process and Their Applications, Vol. 112, No. 1, 2004, pp. 53-78. |

[20] | K. C. Yuen, G. J. Wang and W. Ng Kai, “Ruin Probabilities for a Risk Process with Sto-chastic Return on Investments,” Stochastic Process and Their Applications, Vol. 110, 2004, pp. 259-274 |

[21] | K. C. Yuen, G. J. Wang and R. Wu, “On the Renewal Risk Process with Stochastic Interest,” Stochastic process and Their Applications, Vol. 116, No. 10, 2006, pp. 1496-1510. |

[22] | G. Temnov, “Risk Process with Random Income,” Journal of Mathematical Sciences, Vol. 123, No. 1, 2004, pp. 3780-3794. doi:10.1023/B:JOTH.0000036319.21285.22 |

Journals Menu

Contact us

customer@scirp.org | |

+86 18163351462(WhatsApp) | |

1655362766 | |

Paper Publishing WeChat |

Copyright © 2022 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.