On a partial integrodifferential equation of Seal’s type

Gordon E. Willmot

Insurance: Mathematics and Economics, 2015, vol. 62, issue C, 54-61

Abstract: In this paper we generalize a partial integrodifferential equation satisfied by the finite time ruin probability in the classical Poisson risk model. The generalization also includes the bivariate distribution function of the time of and the deficit at ruin. We solve the partial integrodifferential equation by Laplace transforms with the help of Lagrange’s implicit function theorem. The assumption of mixed Erlang claim sizes is then shown to result in tractable computational formulas for the finite time ruin probability as well as the bivariate distribution function of the time of and the deficit at ruin. A more general partial integrodifferential equation is then briefly considered.

Keywords: Finite time ruin probability; Deficit at ruin; Time of ruin; Lagrange’s implicit function theorem; Lundberg’s fundamental equation; Mixed Erlang distribution (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:62:y:2015:i:c:p:54-61

DOI: 10.1016/j.insmatheco.2015.03.004

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