Abstract
In the dual model, we allow the surplus process to continue if the surplus falls below zero. By introducing the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process, we obtain the probability of hitting the zero point. Further, we derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus and present some examples with an exponential individual jump amount distribution.
Original language | English |
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Pages (from-to) | 591-600 |
Number of pages | 10 |
Journal | Applied Stochastic Models in Business and Industry |
Volume | 24 |
Issue number | 6 |
DOIs | |
Publication status | Published - Nov 2008 |
Keywords
- Compound poisson risk process
- Dual model
- Hitting probability
- Ruin probability
- Total duration of negative surplus