Upper bounds for ruin probabilities in two dependent risk models under rates of interest.

*(English)*Zbl 1226.91082Summary: We consider two discrete-time risk models, in which dependent structures of the payments and the interest force are considered. Two autoregressive moving-average (ARMA) models are introduced to model the premiums and rates of interest, and the claims are assumed to be independent. Generalized Lundberg inequalities for the ruin probabilities are derived by using renewal recursive technique, which extend some known results.

##### MSC:

91G40 | Credit risk |

91G30 | Interest rates, asset pricing, etc. (stochastic models) |

91B30 | Risk theory, insurance (MSC2010) |

##### Keywords:

ruin probability; rate of interest; integral equation; lundberg bound; renewal recursive technique
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\textit{D. Yao} and \textit{R. Wang}, Appl. Stoch. Models Bus. Ind. 26, No. 4, 362--373 (2010; Zbl 1226.91082)

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##### References:

[1] | Gerber, Ruin theory in the linear model, Insurance: Mathematics and Economics 1 pp 177– (1982) · Zbl 0505.62086 |

[2] | Yang, Martingale method for ruin probability in an autoregressive model with constant interest rate, Probability in the Engineering and Informational Sciences 17 (2) pp 183– (2003) · Zbl 1065.62182 |

[3] | Gerber, Martingale in risk theory, Mitteilungen der Schweizer Vereinigung der Versicherungsmathematiker 73 pp 205– (1973) · Zbl 0278.60047 |

[4] | Paulsen, Risk theory in a stochastic economic environment, Stochastic Process and Their Applications 46 pp 327– (1993) · Zbl 0777.62098 |

[5] | Sundt, Ruin estimates under interest force, Insurance: Mathematics and Economics 16 pp 7– (1995) · Zbl 0838.62098 |

[6] | Sundt, The adjustment function in ruin estimates under interest force, Insurance: Mathematics and Economics 19 pp 85– (1997) · Zbl 0910.62107 |

[7] | Yang, Non-exponential bounds for ruin probability with interest effect included, Scandinavian Actuarial Journal 1 pp 66– (1998) |

[8] | Cai, Ruin probabilities with dependent rates of interest, Journal of Applied Probability 39 pp 312– (2002) · Zbl 1007.60096 |

[9] | Cai, Ruin probabilities with a Markov chain interest model, Insurance: Mathematics and Economics 35 pp 513– (2004) · Zbl 1122.91340 |

[10] | Cai, Discrete time risk models under rates of interest, Probability in the Engineering and Informational Sciences 16 pp 309– (2002) · Zbl 1031.91057 |

[11] | Cai, Ruin probabilities and penalty functions with stochastic rates of interest, Stochastic Processes and Their Applications 112 pp 53– (2004) · Zbl 1070.60043 |

[12] | Yao, Exponential bounds for ruin probability in two moving average risk models with constant interest rate, Acta Mathematica Sinica, English Series 24 (2) pp 319– (2008) · Zbl 1143.62071 |

[13] | Cao, The NBUC and NWUC classes of life distributions, Journal of Applied Probability 28 pp 473– (1991) · Zbl 0729.62096 |

[14] | Willmot, Lundberg Approximations for Compound Distributions with Insurance Application (2001) · doi:10.1007/978-1-4613-0111-0 |

[15] | Rolski, Stochastic Processes for Insurance and Finance (1999) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.