Surplus Analysis of Sparre Andersen Insurance Risk Processes by Gordon E. Willmot & Jae-Kyung Woo

Author:Gordon E. Willmot & Jae-Kyung Woo
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.78)

where are constants. Then inversion of (5.78) yields

(5.79)

While the Gerber-Shiu function given by (5.79) is of a simple form, it remains to determine the quantities and for . Henceforth, we assume that for and for are all distinct. Then from (5.73),

which is a polynomial of degree at most in s. This in turn implies that is a polynomial of degree n, with (leading) coefficient of equal to 1. But from (5.77), is a root of for , and is thus a root of this polynomial. Hence, the polynomial must be , i.e.

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