Other papers

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When can accident years be regarded as development years?

When can accident years be regarded as development years? By Glen Barnett, Ben Zehnwirth and Eugene Dubossarsky.

The chain ladder (volume-weighted average development factor) is perhaps the most widely used of the link ratio (age-to-age development factor) techniques, being popular among actuaries in many countries. The chain ladder technique has a number of interesting properties. We present one such property, which indicates that the chain ladder doesn't distinguish between accident years and development years. While we have not seen a proof of this property in English language journals, it appears in Dannenburg, Kaas and Usman [2]. The result is also discussed in Kaas et al. [3]. We give a simple proof that the chain ladder possesses this property and discuss its implications for the chain ladder technique. It becomes clear that the chain ladder does not capture the structure of real triangles.

Solvency II - you need ICRFS-Plus™

ICRFS-Plus™ is the only software that satisfies Solvency II within a sound statistical framework. The models include both process variability and parameter uncertainty.

Claims reserving - some thoughts about principles and methodologies

Claims Reserving - Some Thoughts About Principles and Methodologies by Henk Jan Prins, Chief Actuary Non Life at ASR Nederlands (pdf, approx. 143kb) is an English translation (with the kind permission of the author) of a paper originally published in Dutch in De Actuaris, January 2004.

For some additional material on the points in the article, see the supplement (pdf, approx. 171kb).

Will your next reserve be your last?

Will Your Next Reserve Increase Be Your Last by Prof. Ben Zehnwirth, Dr Julie Sims and Mark Shapland, President of ACTSoft Training Solutions in St. Louis, has been published in CONTINGENCIES, the publication by the American Academy of Actuaries in the Jan/Feb 2004 issue on Page 40-44 (PDF).

Illustration on why ratios do not capture structure

Click here for a simple illustration of why link ratio methods don't capture the structure in the data and don't predict well.

Claims Reserving - Should Ratios be Used?

Claims Reserving - Should Ratios be Used? by Drs. Barnett and Zehnwirth (ClaimsReservingRatios.pdf - 138kb)

Lack of Predictive Power of Development Factor Techniques in Loss Reserving

This article presents regression methodology that can be used to test assumptions made by the standard ratio techniques. The methodology is easy to follow and could be implemented simply in a spreadsheet program.

The methodology demonstrates the lack of predictive power of development factor techniques for most, if not all, cumulative arrays.

Pricing and Reserving Multiple Excess Layers

Patterns and changing trends among several excess-type layers on the same business tend to be closely related. The changes in trend often occur at the same time in each layer. Therefore a good model for the changing trends in the ground-up data will often be a good model for the various layers. As might be expected, after adjusting for the trends, the corresponding values in each layer are still generally correlated. These relationships among layers should be taken into account when reserving or pricing excess layers.

We describe a framework within which such relationships can be explicitly incorporated and taken account of when reserving or pricing several excess layers. This framework allows for reserving and pricing for multiple layers with changes in trends in the same periods, correlations between layers, and possibly equal trends or trend changes across layers.

Click here to view the paper. (ReservingLayers.pdf - 186kb)

Investment Returns and Inflation Models: Some Australian Evidence

(British Actuarial Journal Vol.5, Part 1 (1999))

The development of stochastic investment models for actuarial and investment applications has become an important area of interest to actuaries. This paper reports the application of some techniques of modern time series and econometric analysis to Australian inflation, share market and interest rate data. It considers unit roots, cointegration and state space models. Some of the results from this analysis are not reflected in published stochastic investment models.

Click here to view this paper. (InvestmentReturn.pdf - 112kb)

Abstract: Predictive Aggregate Claims Distribution

Predictive Aggregate Claims Distribution

(Published in Journal of Risk and Insurance 65, 689-709 (1998))

In the collective risk model we use the objective Bayesian approach to calculate predictive aggregate claims distributions. Very often this is equivalent to the profile predictive likelihood approach, but the former is more straightforward to apply, and accordingly we use it as a pragmatic device. We compare the predictive distributions with fitted distributions which take no account of parameter uncertainty and show that actuarial functions such as premiums can be substantially understated if parameter uncertainty is ignored. We illustrate the situation when the moments of the predictive individual claim amount distribution do not exist and we discuss ways of applying such distributions to insurance problems.

Calculating Market Value Margin (MVM) using the Cost of Capital method

Follow the link below for a detailed treatment of MVM for the Solvency Capital requirement (SCR) with ICRFS-Plus, incorporating the concepts of Fair Value and Cost of Capital. In particular we show the difference between a one-year and an ultimate horizon, at a given solvency level. Solvency II mandates a one-year horizon at the 99.5% level.

An ICRFS-Plus Excel Macro can be downloaded from the same page, which enables ICRFS-Plus users to apply these calculations to their own data.

For a detailed description of MVM Calculator information click here.

Look Ahead Stats

Two simple thought-experiments briefly explain the concept of look-ahead statistics:
we don't know future outcomes, but we can know how our outlook would change if we had
some partial results.

This knowledge can be cashed out as precise measures of conditional variability.

Click here to view the paper.

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