# Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

• Volume: 35, Issue: 4, page 359-380
• ISSN: 1310-6600

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## Abstract

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2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the nth arrival, the regression curve of R on S predicts ruin arrival time when the premium intensity c is less than rm whatever be the initial reverve.

## How to cite

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Dia, Galaye, and Kone, Abdoulaye. "Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast." Serdica Mathematical Journal 35.4 (2009): 359-380. <http://eudml.org/doc/281529>.

@article{Dia2009,
abstract = {2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the nth arrival, the regression curve of R on S predicts ruin arrival time when the premium intensity c is less than rm whatever be the initial reverve.},
author = {Dia, Galaye, Kone, Abdoulaye},
journal = {Serdica Mathematical Journal},
keywords = {Point Process; Regressogram; Superposition; Claim Amount; Aggregate Claim Amount; Mean Inter-Arrival Claim Intensity; Mean Intensity of the Claim Process; Ruin Time; regressogram; superposition; claim amount; aggregate claim amount; mean inter-arrival claim intensity; mean intensity; ruin time},
language = {eng},
number = {4},
pages = {359-380},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast},
url = {http://eudml.org/doc/281529},
volume = {35},
year = {2009},
}

TY - JOUR
AU - Dia, Galaye
AU - Kone, Abdoulaye
TI - Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
JO - Serdica Mathematical Journal
PY - 2009
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 4
SP - 359
EP - 380
AB - 2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the nth arrival, the regression curve of R on S predicts ruin arrival time when the premium intensity c is less than rm whatever be the initial reverve.
LA - eng
KW - Point Process; Regressogram; Superposition; Claim Amount; Aggregate Claim Amount; Mean Inter-Arrival Claim Intensity; Mean Intensity of the Claim Process; Ruin Time; regressogram; superposition; claim amount; aggregate claim amount; mean inter-arrival claim intensity; mean intensity; ruin time
UR - http://eudml.org/doc/281529
ER -

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