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Published: January 24,2024

This paper studies the risk process where the individual claim amount density and the interclaim time density are assumed to be arbitrary. It uses the renewability of the risk process at the time of claims and the cumulative law of mathematical expectation to introduce a defective renewal equation satisfied by the joint moments of the surplus immediately before ruin and the deficit at ruin. From this equation, an explicit expression for the above joint moments (including the ruin probability) is obtained by the Laplace transform. Explicit expressions for the ruin probability are given for the case where the claim amount distribution is exponential, and numerical examples are given to analyze the effect of the relevant parameters on the ruin probability under the conditions that the interclaim times follow a Gamma distribution and a generalized Gamma distribution, respectively.

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**Joint Moments of Surplus Immediately Before Ruin and Deficit at Ruin in the Renewal Risk Model**

**How to cite this paper:** Jiayu Wang, Houchun Wang. (2023) Joint Moments of Surplus Immediately Before Ruin and Deficit at Ruin in the Renewal Risk Model. *Journal of Applied Mathematics and Computation*, **7**(**4**), 483-489.

DOI: http://dx.doi.org/10.26855/jamc.2023.12.008

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*k*,*k*) Model^{2} - Joint Moments of Surplus Immediately Before Ruin and Deficit at Ruin in the Renewal Risk Model