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On the distribution of the duration of negative surplus. (English) Zbl 0864.62069
The objective of this paper is to calculate the distribution of the duration of negative surplus, for both single periods and total duration. We will do this in two ways. First, we establish a formula for the density function of the duration of a single period of negative surplus. This leads to the distribution function which we apply in a recursion formula for the distribution function of the total duration of negative surplus. Second, we find results for a discrete time risk model and use these results to approximate the relevant quantities in the classical continuous time model.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E15 Exact distribution theory in statistics
91B30 Risk theory, insurance (MSC2010)
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