On the Density and Moments of the Time of Ruin with Exponential Claims

Steve Drekic · Gordon E. Willmot

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

Abstract

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.

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2000Ruin Probabilities 2001Lundberg Approximations for Compound Distributions with Insurance Applications 2000The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

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2005Phase-type Approximations to Finite-time Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models 2011Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions 2009On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model 2005The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims

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