Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models.

*(English)*Zbl 1231.91157Summary: The structure of various Gerber-Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and interclaim times is examined. The penalty function is assumed to depend on some or all of the surplus immediately prior to ruin, the deficit at ruin, the minimum surplus before ruin, and the surplus immediately after the second last claim before ruin. Defective joint and marginal distributions involving these quantities are derived. Many of the properties in the Sparre Andersen model without dependence are seen to hold in the present model as well. A discussion of Lundberg’s fundamental equation and the generalized adjustment coefficient is given, and the connection to a defective renewal equation is considered. The usual Sparre Andersen model without dependence is also discussed, and in particular the case with exponential claim sizes is considered.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

60K10 | Applications of renewal theory (reliability, demand theory, etc.) |

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

##### Keywords:

defective renewal equation; compound geometric distribution; ladder height; Lundberg’s fundamental equation; generalized adjustment coefficient; Cramer’s asymptotic ruin formula; Esscher transform; last interclaim time; NBU
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\textit{E. C. K. Cheung} et al., Insur. Math. Econ. 46, No. 1, 117--126 (2010; Zbl 1231.91157)

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##### References:

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