IBNR models with random delay distributions.

Neuhaus, Walther

doi:10.1016/0167-6687(93)90899-z

Cited by 6 publications

(4 citation statements)

References 4 publications

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“…Works in this direction are due to Waters and Papatriandafylou (1985), Arjas (1989), Neuhaus (1992), and Norberg (1993). More recently, Mikosch (1995a) and(1995b) proposed to describe delayed claims in terms of Poisson shot noise processes.…”

Section: Introductionmentioning

confidence: 98%

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

2007

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Let us consider a risk process with reserve-dependent premium rate and delayed claims. Consider a class of risk processes derived from the original one via scaling in a slow Markov walk sense. In this paper we prove sample path large deviations for the class of risk processes. As a consequence, we give exact asymptotics for the logarithm of the ruin probabilities and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of the ruin probability

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Section: Introductionmentioning

confidence: 98%

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

2007

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“…These liabilities refer to incidents which have already occurred and will become the subject of claims in the future, but have not yet been reported to the insurer. Stochastic models for this kind of claims, which require payments over several years until they are finally settled, have been proposed by Waters and Papatriandafylou (1985), Arjas (1989), Neuhaus (1992), Norberg (1993), Klüppelberg and Mikosch (1995) and Brémaud (2000). In particular, Klüppelberg and Mikosch (1995) propose the shot-noise process as a natural model for delay in claim settlement.…”

Section: Introductionmentioning

confidence: 98%

Asymptotic results for perturbed risk processes with delayed claims

Macci

Torrisi

2004

Insurance: Mathematics and Economics

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“…, n. In the above log-ANOVA, log-ANCOVA and log-SS models, claim counts and inflation rates can be incorporated into the models. See Hesselager [13], Neuhaus [21] and Haastrup and Arjas [11] and Ntzoufras and Dellaportas [22] for details.…”

Section: State Space Modelsmentioning

confidence: 98%

Robust Bayesian analysis of loss reserving data using scale mixtures distributions

Choy

Chan

Makov

2015

Journal of Applied Statistics

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It is vital for insurance companies to have appropriate levels of loss reserving to pay outstanding claims and related settlement costs. With many uncertainties and time lags inherently involved in the claims settlement process, loss reserving therefore must be based on estimates. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserving. This paper extends the conventional normal error distribution in loss reserving modeling to a range of heavy-tailed distributions which are expressed by certain scale mixtures forms. This extension enables robust analysis and, in addition, allows an efficient implementation of Bayesian analysis via Markov chain Monte Carlo simulations. Various models for the mean of the sampling distributions, including the log-Analysis of Variance (ANOVA), log-Analysis of Covariance (ANCOVA) and state space models, are considered and the straightforward implementation of scale mixtures distributions is demonstrated using OpenBUGS.

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IBNR models with random delay distributions.

Cited by 6 publications

References 4 publications

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

Asymptotic results for perturbed risk processes with delayed claims

Robust Bayesian analysis of loss reserving data using scale mixtures distributions

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