Loss Reserving: Past, Present and Future

Abstract

The paper reviews the development of loss reserving models over the past, classifying them according to an elementary taxonomy. The taxonomic components include (1) the algebraic structure of the model, (2) the form of its parameter estimation, (3) whether or not it is explicitly stochastic, and (4) whether or not its parameters evolve over time. Particular attention is given to one of the higher species of model, involving complex structure, optimal estimation, and evolutionary parameters. A generalisation of the Kalman filter is considered as a basis of adaptive loss reserving in this case. Real life numerical examples are provided. Some implications of this type of data analysis for loss reserving are discussed, with particular reference to the form of data set used. The use of triangular arrays is questioned, and alternatives examined. Again, real life numerical examples are provided.

State Space Models and the Kalman-Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

“…In the first category, the authors De Jong and Zehnwirth (1983), Wright (1990), Zehnwirth (1997), Taylor et al (2003) and Pang and He (2012) mainly use variations on the Hoerl curve to model the claims data over the development years. The general exponential-logarithmic Hoerl curve is given as β j = exp(κj + δ log j) with development year parameter β j for all j = 0, .…”

“…Two of these models (Verrall (1989), Li (2006)) are based on the calendar year approach, and the other two models (Atherino et al (2010), Alpuim and Ribeiro (2003)) consider detached approaches. As for accident year and development year approaches, they can only be found in Taylor et al (2003) and De Jong and Zehnwirth (1983). However, these approaches have no significant advantages compared to the calendar year approach, so they are not introduced in this paper.…”

Calculating insurance claim reserves with fuzzy regression

“…In [27,45,49] wide surveys of these methods can be consulted. According to [46], stochastic methods date back to the middle 1970s. They are more complete and sophisticated than classical methods because, as it is pointed out in [23], they provide not only a fair value for the reserves but also their variability (i.e.…”

Um Modelo Poisson-Lognormal Para Previsão Da Quantidade Ibnr via Micro-Dados

“…Taylor (2003) afirma que a necessidade de agrupar os dados vinha da limitação computacional do passado, quando não era possível analisar os dados no formato não agregado. Com a evolução da capacidade computacional, England e Verrall (2002) também acreditam que se torna questionável examinar os dados agregados e assim perder informações importantes que poderiam ser utilizadas para produzir uma melhor estimativa e ajudar a associar uma distribuição a esta reserva.…”