A continuous-time model for claims reserving

T. Rolski, and A. Tomanek. "A continuous-time model for claims reserving." Applicationes Mathematicae 41.4 (2014): 277-300. <http://eudml.org/doc/279899>.

@article{T2014,
abstract = {Prediction of outstanding liabilities is an important problem in non-life insurance. In the framework of the Solvency II Project, the best estimate must be derived by well defined probabilistic models properly calibrated on the relevant claims experience. A general model along these lines was proposed earlier by Norberg (1993, 1999), who suggested modelling claim arrivals and payment streams as a marked point process. In this paper we specify that claims occur in [0,1] according to a Poisson point process, possibly non-homogeneous, and that each claim initiates a stream of payments, which is modelled by a non-homogeneous compound Poisson process. Consecutive payment streams are i.i.d. and independent of claim arrivals. We find estimates for the total payment in an interval (v,v+s], where v≥1, based upon the total payment up to time v. An estimate for Incurred But Not Reported (IBNR) losses is also given.},
author = {T. Rolski, A. Tomanek},
journal = {Applicationes Mathematicae},
keywords = {non-homogeneous Poisson process; claim reserving; FFT; IBNR losses; saddlepoint approximation},
language = {eng},
number = {4},
pages = {277-300},
title = {A continuous-time model for claims reserving},
url = {http://eudml.org/doc/279899},
volume = {41},
year = {2014},
}

TY - JOUR
AU - T. Rolski
AU - A. Tomanek
TI - A continuous-time model for claims reserving
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 4
SP - 277
EP - 300
AB - Prediction of outstanding liabilities is an important problem in non-life insurance. In the framework of the Solvency II Project, the best estimate must be derived by well defined probabilistic models properly calibrated on the relevant claims experience. A general model along these lines was proposed earlier by Norberg (1993, 1999), who suggested modelling claim arrivals and payment streams as a marked point process. In this paper we specify that claims occur in [0,1] according to a Poisson point process, possibly non-homogeneous, and that each claim initiates a stream of payments, which is modelled by a non-homogeneous compound Poisson process. Consecutive payment streams are i.i.d. and independent of claim arrivals. We find estimates for the total payment in an interval (v,v+s], where v≥1, based upon the total payment up to time v. An estimate for Incurred But Not Reported (IBNR) losses is also given.
LA - eng
KW - non-homogeneous Poisson process; claim reserving; FFT; IBNR losses; saddlepoint approximation
UR - http://eudml.org/doc/279899
ER -