Point Process Regressogram Superposition Claim Amount Aggregate Claim Amount Mean Inter-Arrival Claim Intensity Mean Intensity of the Claim Process Ruin Time
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 35, No 4, (2009), 359p-380p
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.