ICFS-Plus: Actuarial Software for the Property and Causality Insurance Industry


CLRS 2014: Correlations vs Common Accident Year and Calendar Year Drivers

We discuss three types of relationships between long tail LOBs; process or volatility correlation, parameter correlation and similar trend structure, equivalently common drivers. Two LOBs or segments have common calendar (accident) year drivers if calendar (accident) year trends change in the same way in the same years. Common drivers are the strongest type of relationships.

Process correlation between two LOBs is spurious unless for each LOB the identified (optimal) model measures the trends in the three directions.Common drivers by accident (underwriting) year have major implications for pricing future accident (underwriting) years.

The single identified (optimal) composite model projects log-normal distributions for each cell in each LOB including correlations between LOBs and within LOBs yielding a wealth of metrics. It facilitates the computation of the Economic Balance Sheet, SII one-year risk horizon metrics including SCR, Technical Provisions and Risk Margins, and variation in mean ultimates on year hence.

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Best Estimates: the ELRF and PTF models

The Extended Link Ratio Family (ELRF) and the Probabilistic Trend Family (PTF) modeling frameworks are described in the paper "Best Estimates for Reserves" (PCAS, 2000, included in CAS Syllabus of Examinations). In ELRF, average weighted link ratios (development factors) are formalized as regression estimators (Mack method), and extended to include other modeling components of interest (eg. intercepts, Murphy method). Resulting benefits include forecast standard error and testing that assumptions made by the model are supported by the data. In the PTF framework a model is built that captures the variation in the incremental loss development array, which is described using trends in the three directions: development period, accident period and calendar period and the variability of the data about the trend structure. The identified model fits (and projects for the future) lognormal distributions to each cell in the development array, conditional on certain explicit assumptions related to the historical experience, which can be amended as desired.

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Modeling of Multiple lines of busines, segments and layers with applications to capital allocation and optimal reinsurance

The MPTF modeling framework is used to design a composite model for multiple incremental loss development arrays. The identified model describes the variability in each array and the relationships between them (a la PTF models).This has applications to modeling multiple lines of business, segments, layers and credibility modeling. Relationships between arrays involve both process correlation and parameter correlation. Clusters of lines of business are designed where correlations between any lines of business in different clusters are zero. An optimal composite model forecasts lognormal distributions for each cell in each loss development array, including the correlations between cells within in an array and between arrays. These induce correlations between forecasts for each pair of accident years, calendar years and aggregates. (This talk assumes the attendees are familiar with the material in the talk "Best Estimates: the ELRF and PTF models" or the paper "Best Estimates for Reserves," PCAS, 2000).

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Build a better Bootstrap: Distributions for the Mack method, related methods and PTF models

The Mack method has become popular as a way of computing standard deviations for volume weighted average link ratios. With the increasing prudential and regulatory need to compute other risk measures such as VaR and T-VaR actuaries have sought access to the complete probability distribution of reserves. To this end one proposed methodology in common use is the statistical Bootstrap.

Here we take a different tack and use the Bootstrap as a way of assessing the worth of any model, including the Mack method, in relation to the original data.

In this talk the Bootstrap technique is first explained in detail. At the heart of the method is a way of using any model to create many alternative datasets (called Bootstrap pseudo datasets) which reproduce key features of the original data.

We compare Bootstrap samples derived from the Mack method with Bootstrap samples based on the optimal PTF model using several real datasets. We find that Bootstrap samples (pseudo data) based on the Mack method (and related methods) do not reflect features in the original data, that is, you can easily distinguish between the real data and the Bootstrap samples. However, you cannot distinguish between Bootstrap samples based on the optimal PTF model and the original data.

The worth of the results derived from Bootstrap technique is directly dependent on the validity of the model for the data.

The powerpoint presentation is available here.

Loss Reserve Upgrades - A Pervasive Myth

Major misconceptions about the loss reserving process are widespread. We debunk a critical loss reserving myth involving loss reserve upgrades that is pervasive in the insurance industry.

The powerpoint presentation is available here, alternatively, an online discussion can be found here.

Solvency II Seminar, Dec 2012

We provide our solution to the Solvency II one-year risk horizon, SCR, Technical Provisions (TP) (Fair Value Liabilities), Market Value Margins (Risk Margins) for the aggregate of long tail LOBs.

The solution is non-recursive, non-circular, tractable and satisfies all the directives (requirements).

Topics include:

  • IFRS4 requirements in respect of fungibility and ring-fencing
  • Three types of correlations between LOBs
  • How do we know if two LOBs have the same economic drivers?
  • Is the economic inflation a principal driver of long tail liability calendar year trends?

The powerpoint presentation is available here.