Journal article
RATIO MONOTONICITY FOR TAIL PROBABILITIES IN THE RENEWAL RISK MODEL
Probability in the engineering and informational sciences, Vol.25(2), pp.171-185
04/2011
Handle:
https://hdl.handle.net/2376/114316
Abstract
A renewal model in risk theory is considered, where $\overline{H}(u,y)$ is the tail of the distribution of the deficit at ruin with initial surplus u and $\overline{F}(y)$ is the tail of the ladder height distribution. Conditions are derived under which the ratio $\overline{H}(u,y)/\overline{F}(u+y)$ is nondecreasing in u for any y≥0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then the above ratio is nondecreasing in u. As a byproduct of this monotonicity, an upper bound and an asymptotic result for $\overline{H}(u,y)$ are derived. Examples are given to illustrate the monotonicity results.
Metrics
12 Record Views
Details
- Title
- RATIO MONOTONICITY FOR TAIL PROBABILITIES IN THE RENEWAL RISK MODEL
- Creators
- Georgios Psarrakos - Department of Statistics and Insurance Science, University of Piraeus, Piraeus 18534, Greece E-mail: gpsarr@unipi.grMichael Tsatsomeros - Department of Mathematics, Washington State University, Pullman, WA 99164-3113, E-mail: tsat@wsu.edu
- Publication Details
- Probability in the engineering and informational sciences, Vol.25(2), pp.171-185
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Cambridge University Press; New York, USA
- Number of pages
- 15
- Identifiers
- 99900547575201842
- Language
- English
- Resource Type
- Journal article