Dos Reis, Alfredo Egídio How long is the surplus below zero? (English) Zbl 0777.62096 Insur. Math. Econ. 12, No. 1, 23-38 (1993). 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) Cited in 55 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:moment generating function; individual claim amount distributions; compound geometric distribution; severity of ruin; probability of ruin; exponential distributions; gamma distributions; compound Poisson continuous-time surplus process; first negative surplus; total duration of negative surplus; Gerber model; martingale method; distributions of time of ruin; zero initial surplus Citations:Zbl 0731.62153 Software:Mathematica PDFBibTeX XMLCite \textit{A. E. Dos Reis}, Insur. Math. Econ. 12, No. 1, 23--38 (1993; Zbl 0777.62096) Full Text: DOI References: [1] Bowers, N. L.; Gerber, H. U.; Hickman, C. J.; Jones, D. A.; Nesbitt, C. J., Actuarial Mathematics (1987), Society of Actuaries: Society of Actuaries Itasca, IL · Zbl 0634.62107 [2] Dickson, D. C.M., On the distribution of the surplus prior to ruin, Insurance: Mathematics & Economics, 11, 3 (1992) · Zbl 0770.62090 [3] Dufresne, F.; Gerber, H. U., The surpluses immediately before and at ruin, and the amount of the claim causing ruin, Insurance: Mathematics & Economics, 7, 193-199 (1988) · Zbl 0674.62072 [4] Gerber, H. U., An Introduction to Mathematical Risk Theory (1979), University of Pennsylvania: University of Pennsylvania Philadelphia, PA, S.S. Huebner Foundation for Insurance Education · Zbl 0431.62066 [5] Gerber, H. U., Mathematical fun with run theory, Insurance: Mathematics & Economics, 7, 15-23 (1988) · Zbl 0657.62121 [6] Gerber, H. U., When does the surplus reach a given target?, Insurance: Mathematics & Economics, 9, 115-119 (1990) · Zbl 0731.62153 [7] Gerber, H. U.; Goovaerts, M. J.; Kaas, R., On the probability and severity of ruin, Astin Bulletin, 17, 151-163 (1987) [8] Wolfram, S., The Advanced Book Program, (Mathematica - A system for doing mathematics by computer (1991), Addison-Wesley: Addison-Wesley Redwood City, CA) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.