Geodesic
Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 359-380.

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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.
Keywords: Point Process, Regressogram, Superposition, Claim Amount, Aggregate Claim Amount, Mean Inter-Arrival Claim Intensity, Mean Intensity of the Claim Process, Ruin Time 
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Dia, Galaye; Kone, Abdoulaye. Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast. Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 359-380. http://geodesic.mathdoc.fr/item/SMJ2_2009_35_4_a2/