scholarly journals A COLLECTIVE RESERVING MODEL WITH CLAIM OPENNESS

2021 ◽  
pp. 1-27
Author(s):  
Mathias Lindholm ◽  
Henning Zakrisson
Keyword(s):  
Linear Models ◽  
Mean Squared Error ◽  
Numerical Illustration ◽  
Generalised Linear Models ◽  
Aggregated Data ◽  
Squared Error ◽  
Analytic Expressions ◽  
Chain Ladder ◽  
The One ◽  
Comparable Quality

Abstract The present paper introduces a simple aggregated reserving model based on claim count and payment dynamics, which allows for claim closings and re-openings. The modelling starts off from individual Poisson process claim dynamics in discrete time, keeping track of accident year, reporting year and payment delay. This modelling approach is closely related to the one underpinning the so-called double chain-ladder model, and it allows for producing separate reported but not settled and incurred but not reported reserves. Even though the introduction of claim closings and re-openings will produce new types of dependencies, it is possible to use flexible parametrisations in terms of, for example, generalised linear models (GLM) whose parameters can be estimated based on aggregated data using quasi-likelihood theory. Moreover, it is possible to obtain interpretable and explicit moment calculations, as well as having consistency of normalised reserves when the number of contracts tend to infinity. Further, by having access to simple analytic expressions for moments, it is computationally cheap to bootstrap the mean squared error of prediction for reserves. The performance of the model is illustrated using a flexible GLM parametrisation evaluated on non-trivial simulated claims data. This numerical illustration indicates a clear improvement compared with models not taking claim closings and re-openings into account. The results are also seen to be of comparable quality with machine learning models for aggregated data not taking claim openness into account.

Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable

1993 ◽  
Vol 9 (1) ◽  
pp. 62-80 ◽  
Author(s):  
Jan F. Kiviet ◽  
Garry D.A. Phillips
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Small Sample ◽  
Large Sample ◽  
Squared Error ◽  
Coefficient Vector ◽  
Lagged Dependent Variable ◽  
Biased Estimators ◽  
The One

The small sample bias of the least-squares coefficient estimator is examined in the dynamic multiple linear regression model with normally distributed whitenoise disturbances and an arbitrary number of regressors which are all exogenous except for the one-period lagged-dependent variable. We employ large sample (T → ∞) and small disturbance (σ → 0) asymptotic theory and derive and compare expressions to O(T−1) and to O(σ2), respectively, for the bias in the least-squares coefficient vector. In some simulations and for an empirical example, we examine the mean (squared) error of these expressions and of corrected estimation procedures that yield estimates that are unbiased to O(T−l) and to O(σ2), respectively. The large sample approach proves to be superior, easily applicable, and capable of generating more efficient and less biased estimators.

COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE

2018 ◽  
Vol 48 (3) ◽  
pp. 1137-1156 ◽  
Author(s):  
Shengwang Meng ◽  
Guangyuan Gao
Keyword(s):  
Linear Models ◽  
Mean Squared Error ◽  
Predictive Distribution ◽  
Compound Poisson ◽  
Poisson Models ◽  
Squared Error ◽  
Run Off ◽  
Mean And Variance ◽  
The Individual ◽  
Over Dispersion

AbstractWe consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

Comparison of some annual forest inventory estimators

2002 ◽  
Vol 32 (11) ◽  
pp. 1992-1995 ◽  
Author(s):  
Paul C Van Deusen
Keyword(s):  
Forest Inventory ◽  
Mean Squared Error ◽  
Moving Average ◽  
Current Status ◽  
Quadratic Growth ◽  
Growth Trends ◽  
Squared Error ◽  
Mixed Estimator ◽  
The One ◽  
Panel Design

Three estimators of current status and trend are compared for an annual interpenetrating panel design. The five-panel annual inventory design is simulated over a 10-year period with flat, increasing, and quadratic growth trends. The simulated comparisons show that the mixed estimator performs well relative to the 5-year moving average in terms of bias and mean squared error in all cases. The one-panel mean can have less bias than the moving average when there is a trend, but it is more variable. The moving average tends to lag evolving trends, which can result in very large bias.

scholarly journals Moving beyond the classic difference-in-differences model: a simulation study comparing statistical methods for estimating effectiveness of state-level policies

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Beth Ann Griffin ◽  
Megan S. Schuler ◽  
Elizabeth A. Stuart ◽  
Stephen Patrick ◽  
Elizabeth McNeer ◽  
...  
Keyword(s):  
Null Hypothesis ◽  
Linear Models ◽  
Type I Error ◽  
Mean Squared Error ◽  
State Level ◽  
Error Rates ◽  
Type I ◽  
Directional Bias ◽  
Squared Error ◽  
Ar Models

Abstract Background Reliable evaluations of state-level policies are essential for identifying effective policies and informing policymakers’ decisions. State-level policy evaluations commonly use a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. More guidance is needed about which set of statistical models perform best when estimating how state-level policies affect outcomes. Methods Motivated by applied state-level opioid policy evaluations, we implemented an extensive simulation study to compare the statistical performance of multiple variations of the two-way fixed effect models traditionally used for DID under a range of simulation conditions. We also explored the performance of autoregressive (AR) and GEE models. We simulated policy effects on annual state-level opioid mortality rates and assessed statistical performance using various metrics, including directional bias, magnitude bias, and root mean squared error. We also reported Type I error rates and the rate of correctly rejecting the null hypothesis (e.g., power), given the prevalence of frequentist null hypothesis significance testing in the applied literature. Results Most linear models resulted in minimal bias. However, non-linear models and population-weighted versions of classic linear two-way fixed effect and linear GEE models yielded considerable bias (60 to 160%). Further, root mean square error was minimized by linear AR models when we examined crude mortality rates and by negative binomial models when we examined raw death counts. In the context of frequentist hypothesis testing, many models yielded high Type I error rates and very low rates of correctly rejecting the null hypothesis (< 10%), raising concerns of spurious conclusions about policy effectiveness in the opioid literature. When considering performance across models, the linear AR models were optimal in terms of directional bias, root mean squared error, Type I error, and correct rejection rates. Conclusions The findings highlight notable limitations of commonly used statistical models for DID designs, which are widely used in opioid policy studies and in state policy evaluations more broadly. In contrast, the optimal model we identified--the AR model--is rarely used in state policy evaluation. We urge applied researchers to move beyond the classic DID paradigm and adopt use of AR models.

scholarly journals Efficient Generalized Ratio-Product Type Estimators for Finite Population Mean with Ranked Set Sampling

2016 ◽  
Vol 42 (3) ◽  
pp. 137-148 ◽  
Author(s):  
V.L. Mandowara ◽  
Nitu Mehta
Keyword(s):  
Mean Squared Error ◽  
Order Approximation ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Power Transformation ◽  
Numerical Illustration ◽  
Population Mean ◽  
Squared Error ◽  
The Mean ◽  
First Order Approximation

In this paper we suggest two modified estimators of the population mean using the power transformation based on ranked set sampling (RSS). The first order approximation of the bias and of the mean squared error of the proposed estimators are obtained. A generalized version of the suggested estimators by applying the power transformation is also presented. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in simple random sampling (SRS). A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.

scholarly journals Credible Claims Reserves: the Benktander Method

2000 ◽  
Vol 30 (2) ◽  
pp. 333-347 ◽  
Author(s):  
Thomas Mack
Keyword(s):  
Stochastic Model ◽  
Mean Squared Error ◽  
The Other ◽  
Bayesian Procedure ◽  
Mean Squared Errors ◽  
Squared Error ◽  
The Mean ◽  
Chain Ladder ◽  
Simple Stochastic Model

AbstractA claims reserving method is reviewed which was introduced by Gunnar Benktander in 1976. It is a very intuitive credibility mixture of Bornhuetter/Ferguson and Chain Ladder. In this paper, the mean squared errors of all 3 methods are calculated and compared on the basis of a very simple stochastic model. The Benktander method is found to have almost always a smaller mean squared error than the other two methods and to be almost as precise as an exact Bayesian procedure.

scholarly journals Ascertaining Time Series Predictability in Process Control – Case Study on Rainfall Prediction

2018 ◽  
Vol 203 ◽  
pp. 07002
Author(s):  
Chandrasekaran Sivapragasam ◽  
Poomalai Saravanan ◽  
Saminathan Balamurali ◽  
Nitin Muttil
Keyword(s):  
Time Series ◽  
Process Control ◽  
Hurst Exponent ◽  
Mean Squared Error ◽  
Rain Gauge ◽  
Natural Phenomenon ◽  
Rainfall Prediction ◽  
Squared Error ◽  
The One

Rainfall prediction is a challenging task due to its dependency on many natural phenomenon. Some authors used Hurst exponent as a predictability indicator to ensure predictability of the time series before prediction. In this paper, a detailed analysis has been done to ascertain whether a definite relation exists between a strong Hurst exponent and predictability. The one-lead monthly rainfall prediction has been done for 19 rain gauge station of the Yarra river basin in Victoria, Australia using Artificial Neural Network. The prediction error in terms of normalized Root Mean Squared Error has been compared with Hurst exponent. The study establishes the truth of the hypothesis for only 6 stations out of 19 stations, and thus recommends further investigation to prove the hypothesis. This concept is relevant for any time series which need to be used for real time process control.

scholarly journals Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Martin M. Kithinji ◽  
Peter N. Mwita ◽  
Ananda O. Kube
Keyword(s):  
Value At Risk ◽  
Mean Squared Error ◽  
Conditional Value At Risk ◽  
Conditional Quantile ◽  
Squared Error ◽  
Quantile Autoregression ◽  
Simulation Results ◽  
The One ◽  
Conditional Quantile Estimator ◽  
Extreme Conditional Quantile

In this paper, we propose an extreme conditional quantile estimator. Derivation of the estimator is based on extreme quantile autoregression. A noncrossing restriction is added during estimation to avert possible quantile crossing. Consistency of the estimator is derived, and simulation results to support its validity are also presented. Using Average Root Mean Squared Error (ARMSE), we compare the performance of our estimator with the performances of two existing extreme conditional quantile estimators. Backtest results of the one-day-ahead conditional Value at Risk forecasts are also given.

A BIFURCATION APPROACH FOR ATTRITIONAL AND LARGE LOSSES IN CHAIN LADDER CALCULATIONS

2013 ◽  
Vol 44 (1) ◽  
pp. 127-172 ◽  
Author(s):  
Ulrich Riegel
Keyword(s):  
Stochastic Model ◽  
Mean Squared Error ◽  
Third Party ◽  
Long Tail ◽  
Squared Error ◽  
The Mean ◽  
Chain Ladder

AbstractWe introduce a stochastic model for the development of attritional and large claims in long-tail lines of business and present a corresponding “chain ladder-like” IBNR method which allows the use of claims payment data for attritional and claims incurred data for large losses. We derive formulas for the mean squared error of prediction and apply the method to a German motor third party liability portfolio.

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