an:00223203
Zbl 0777.62096
Dos Reis, Alfredo Eg??dio
How long is the surplus below zero?
EN
Insur. Math. Econ. 12, No. 1, 23-38 (1993).
00012997
1993
j
62P05
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
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 [\textit{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.
L.S.Ioffe (Haifa)
Zbl 0731.62153