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Risk models based on time series for count random variables. (English) Zbl 1218.91074
Summary: We generalize the classical discrete time risk model by introducing a dependence relationship in time between the claim frequencies. The models used are the Poisson autoregressive model and the Poisson moving average model. In particular, the aggregate claim amount and related quantities such as the stop-loss premium, value at risk and tail value at risk are discussed within this framework.

MSC:
91B30 Risk theory, insurance (MSC2010)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
QRM
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