IBNR models with random delay distributions

Neuhaus, Walther

doi:10.1080/03461238.1992.10413901

“…The ideas have been developed further by HESSELAGER and WITTING (1988), who specify assumptions about stochastic variation in the development pattern from one year to another. This issue has been pursued also in a recent paper by NEUHAUS (1992). The present paper carries on in two directions of increasing generality.…”

Section: A Objective Of the Study And Relations To Existing Actuariamentioning

confidence: 89%

“…a portfolio of fire insurance policies where the fire peril and the typical claim size vary substantially from one house to another, depending on size of the building, building materials, fire preventing measures, and possibly other characteristics. As explained by NORBERG and SUNDT (1985), in such a situation one cannot rely on aggregate statistics on claims frequencies and claim sizes for the portfolio as a whole: changes in the composition of the portfolio may cause considerable changes of the claims process in the course of time.…”

Section: Observable Risk Characteristics Modelled By Covariatesmentioning

confidence: 99%

Prediction of Outstanding Liabilities in Non-Life Insurance

Norberg

¹

1993

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A fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.

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“…a portfolio of fire insurance policies where the fire peril and the typical claim size vary substantially from one house to another, depending on size of the building, building materials, fire preventing measures, and possibly other characteristics. As explained by NORBERG and SUNDT (1985), in such a situation one cannot rely on aggregate statistics on claims frequencies and claim sizes for the portfolio as a whole: changes in the composition of the portfolio may cause considerable changes of the claims process in the course of time.…”

Section: Observable Risk Characteristics Modelled By Covariatesmentioning

confidence: 99%

Prediction of outstanding liabilities in non-life insurance.

Norberg

¹

1993

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

A fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.

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“…In recent years a number of papers on loss reserving have appeared where the delay probabilities for observations in discrete time are assumed to vary between occurrence years. In these papers (HESSELAGER and WITTING, 1988;NEUHAUS, 1992;LAWLESS, 1994; HESS and SCHMIDT, 1994a, b) the variations are treated as random fluctuations between occurrence years and are modelled by a Dirichlet distribution which is a mathematically very convenient construct. In the present paper it is shown that fluctuations induced in the discretizing process possess a special structure and that these fluctuations can not be described by a Dirichlet distribution in a reasonable manner.…”

Section: Introductionmentioning

confidence: 99%