Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process

Yebin Cheng · Qihe Tang

67 citations0/0 files storedNorth American Actuarial Journal

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Probability and Risk Models Probability and Statistical Research Insurance, Mortality, Demography, Risk Management

Abstract

This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends to infinity. Also, we show the joint probability density function of the surplus before ruin and the deficit at ruin.

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References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1987Applied Probability and Queues 1998On the Time Value of Ruin 1986Actuarial Mathematics.1982Estimates for the probability of ruin with special emphasis on the possibility of large claims 2001On the time to ruin for Erlang(2) risk processes 1977Asymptotic behaviour of Wiener-Hopf factors of a random walk

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