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How long is the surplus below zero? (English) Zbl 0777.62096
For the classical compound Poisson continuous-time surplus process the following evaluations are considered: duration of the first negative surplus, duration of any other negative surplus, total duration of negative surplus.
The author develops the Gerber model [H. U. Gerber, Insur. Math. Econ. 9, No. 2/3, 115-119 (1990; Zbl 0731.62153)], using his martingale method. The symmetry between the distributions of time of ruin and duration of a negative surplus is discussed for the zero initial surplus. Finally, the author presents two examples, considering exponential and gamma \((2,\beta)\) distributions.
Reviewer: L.S.Ioffe (Haifa)

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
Mathematica
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References:
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