18 research outputs found
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On the relationship between classical chain ladder and granular reserving
We connect classical chain ladder to granular reserving. This is done by defining explicitly how the classical run-off triangles are generated from individual iid observations in continuous time. One important result is that the development factors have a one to one correspondence to a histogram estimator of a hazard running in reversed development time. A second result is that chain ladder has a systematic bias if the row effect has not the same distribution when conditioned on any of the aggregated periods. This means that the chain ladder assumptions on one level of aggregation, say yearly, are different from the chain ladder assumptions when aggregated in quarters and the optimal level of aggregation is a classical bias variance trade-off depending on the data-set. We introduce smooth development factors arising from non-parametric hazard kernel smoother improving the estimation significantly
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A comparison of in-sample forecasting methods
In-sample forecasting is a recent continuous modification of well-known forecasting methods based on aggregated data. These aggregated methods are known as age-cohort methods in demography, economics, epidemiology and sociology and as chain ladder in non-life insurance. Data is organized in a two-way table with age and cohort as indices, but without measures of exposure. It has recently been established that such structured forecasting methods based on aggregated data can be interpreted as structured histogram estimators. Continuous in-sample forecasting transfers these classical forecasting models into a modern statistical world including smoothing methodology that is more efficient than smoothing via histograms. All in-sample forecasting estimators are collected and their performance is compared via a finite sample simulation study. All methods are extended via multiplicative bias correction. Asymptotic theory is being developed for the histogram-type method of sieves and for the multiplicatively corrected estimators. The multiplicative bias corrected estimators improve all other known in-sample forecasters in the simulation study. The density projection approach seems to have the best performance with forecasting based on survival densities being the runner-up
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Self-selection and risk sharing in a modern world of lifelong annuities - Abstract of the London Discussion
This abstract relates to the following paper: Gerrard, R., Hiabu, M., Kyriakou, I. and Nielsen, J. P. (2018) Self-selection and risk sharing in a modern world of lifelong annuities ‐ Abstract of the London Discussion. British Actuarial Journal. Cambridge University Press, 23. doi: 10.1017/S135732171800020X
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Self-selection and risk sharing in a modern world of life-long annuities
Communicating a pension product well is as important as optimising the financial value. In a recent study, we showed that up to 80% of the value of a pension lump sum could be lost if customer communication failed. In this paper, we extend the simple customer interaction of the earlier contribution to the more challenging lifetime annuity case. Using a simple mobile phone device, the pension customer can select the life-long optimal investment strategy within minutes. The financial risk trade-off is presented as a trade-off between the pension paid and the number of years the life-long annuity is guaranteed. The pension payment decreases when investment security increases. The necessary underlying mathematical financial hedging theory is included in the stud
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In-sample forecasting: structured models and reserving
In most developed countries, the insurance sector accounts for around eight percent of the GDP. In Europe alone the insurers liabilities are estimated at around e900 billion. Every insurance company regularly estimates its liabilities and reports them, in conjunction with statements about capital and assets, to the regulators. The liabilities determine the insurers solvency and also its pricing and investment strategy. The new EU directive, Solvency II, which came into effect in the beginning of 2016, states that those liabilities should be estimated with ‘realistic assumption’ using ‘relevant actuarial and statistical methods’. However, modern statistics has not found its way in the reserving departments of today’s insurance companies. This thesis attempts to contribute to the connection between the world of mathematical statistics and the reserving practice in general insurance. As part of this thesis, it is in particular shown that today’s reserving practice can be understood as a non-parametric estimation approach in a structured model setting. The forecast of future claims is done without the use of exposure information, i.e., without knowledge about the number of underwritten policies. New statistical estimation techniques and properties are derived which are build from this motivating application
Replicating and extending chain-ladder via an age-period-cohort structure on the claim development in a run-off triangle
This paper introduces yet another stochastic model replicating chain-ladder
estimates and furthermore considers extensions that add flexibility to the
modeling. In its simplest form, the proposed model replicates the
chain-ladder's development factors using a GLM model with averaged hazard rates
running in reversed development time as response. This is in contrast to the
existing reserving literature within the GLM framework where claim amounts are
modeled as response. Modeling the averaged hazard rate corresponds to modeling
the claim development and is arguably closer to the actual chain-ladder
algorithm. Furthermore, since exposure does not need to be modeled, the model
only has half the number of parameters compared to when modeling the claim
amounts. This lesser complexity can be used to easily introduce model
extensions that may better fit the data. We provide a new R-package,
, where the models are implemented and can be fed with
run-off triangles. We conduct an empirical study on 30 publicly available
run-off triangles making a case for the benefit of having in
the actuary's toolbox
Identifiability and estimation of the competing risks model under exclusion restrictions
The non-identifiability of the competing risks model requires researchers to
work with restrictions on the model to obtain informative results. We present a
new identifiability solution based on an exclusion restriction. Many areas of
applied research use methods that rely on exclusion restrcitions. It appears
natural to also use them for the identifiability of competing risks models. By
imposing the exclusion restriction couple with an Archimedean copula, we are
able to avoid any parametric restriction on the marginal distributions. We
introduce a semiparametric estimation approach for the nonparametric marginals
and the parametric copula. Our simulation results demonstrate the usefulness of
the suggested model, as the degree of risk dependence can be estimated without
parametric restrictions on the marginal distributions
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Validating the double chain ladder stochastic claims reserving model
Double chain ladder, introduced by Martínez-Miranda et al. (2012), is a statistical model to predict outstanding claim reserve. Double chain ladder and Bornhuetter-Ferguson are extensions of the originally described double chain ladder model which gain more stability through including expert knowledge via an incurred claim amounts triangle. In this paper, we introduce a third method, the incurred double chain ladder, which replicates the popular results from the classical chain ladder on incurred data. We will compare and validate these three using two data sets from major property and casualty insurers
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Global Polynomial Kernel Hazard Estimation
This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail