Abstract
Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. When the individual claims have a phase-type distribution, the deficit at ruin is also of phase-type.
Keywords: Sparre Andersen Model, Ladder Height, Maximal Aggregate Loss, Compound Geometric Convolution, Defective Renewal Equation, Phase-type Distribution, Dfr
Volume
No. 4
Page
241-255
Year
2004
Categories
Actuarial Applications and Methodologies
Capital Management
Capital Requirements
Actuarial Applications and Methodologies
Dynamic Risk Modeling
Solvency Analysis
Financial and Statistical Methods
Loss Distributions
Financial and Statistical Methods
Statistical Models and Methods
Publications
Scandinavian Actuarial Journal
