TY - JOUR
T1 - Modelling Outstanding Claims with Mixed Compound Processes in insurance
AU - Clemente, Gian Paolo
AU - Savelli, Nino
AU - Zappa, Diego
PY - 2019
Y1 - 2019
N2 - In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analysed by exploiting the Fisher-Lange average cost method.
AB - In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analysed by exploiting the Fisher-Lange average cost method.
KW - Average cost method
KW - Collective risk model
KW - Reserve Risk
KW - Solvency II
KW - Stochastic models for claims reserve
KW - Average cost method
KW - Collective risk model
KW - Reserve Risk
KW - Solvency II
KW - Stochastic models for claims reserve
UR - http://hdl.handle.net/10807/129736
M3 - Article
SN - 1913-9004
SP - 123
EP - 138
JO - INTERNATIONAL BUSINESS RESEARCH
JF - INTERNATIONAL BUSINESS RESEARCH
ER -