## THE PROJECT

On 30 June 2013, the Australian Research Council (ARC) awarded funding to a project titled Modelling claim dependencies for the general insurance industry with economic capital in view: an innovative approach with stochastic processes. The project is overseen primarily by the three authors as principal researchers.

This rather turgid title was deliberately selected to contain all the project’s relevant keywords, and so push all the buttons required to secure funding in an environment that is extremely competitive (see below). In the present article, the project will be referred to as simply the claim dependency project.

## PURPOSE

There are two major areas in which claim dependencies affect economic capital and the statutory requirements surrounding it. Broadly, these relate to:

• risk margins in claims reserving; and
• capital margins.

Prudential Standard GPS 320 associated with the Insurance Act 1973 requires that insurance liabilities be ‘determined on a basis that is intended to value the insurance liabilities of the insurer at (at least) a 75 per cent level of sufficiency’. The difference between this estimate of liabilities and the central estimate (i.e. mean forecast) is referred to as the

The Standard permits the risk margin to recognise diversification between different segments of business, i.e. the lack of total dependency between those segments. The greater the degree of diversification, the less a risk margin, calculated according to the above 75% value at risk (Var). Thus, quantification of diversification requires formulation and measurement of the dependency between segments.

In the case of capital margins estimated by means of an internal model, Prudential Practice Guide GPG 113 states that the minimum capital requirement is a 99.5% VaR, but this time in respect of total net assets and taking account of all associated risks. There is thus a parallel between computation of risk margins and capital margins in that both apply VaR methodology, and therefore both require dependencies between their components to be formulated and measured.

Indeed, GPG 113 essentially requires that these dependencies be incorporated in an internal model.

The purpose of the claim dependency project is to consider ways and means of enhancing the modelling of dependencies in the stochastic claims models available to insurers in the contexts just described.

## ARC AND FUNDING

The ARC manages the National Competitive Grants Program, which provides Federal funding for research projects that are assessed as meritorious.

Apart from health research schemes, there are two main types of project that may attract funding, known as Discovery Projects and Linkage Projects respectively. The claim dependency project falls within the latter category.

The selection process for Linkage Projects is extremely competitive. The 2012/13 round included 785 applications. In the Banking, Finance, and Investment category, only two applications, including our own, were successful.

The Linkage Projects scheme provides funding to support projects that are collaborative between higher education researchers and other parts of the so-called national innovation system, which includes corporations. Each project involves collaboration between academia and one or more Partner Organisations (POs).

In the case under discussion, the three principal researchers from UNSW collaborate with the following POs:

• Allianz;

• Insurance Australia Group; and

• Suncorp.

The claim dependency project is a three-year project, covering essentially the calendar years 2014 to 2016.

Funding is provided by the ARC and POs. Although funding requested from the ARC cannot exceed that offered by the POs, much of the latter may be provided in kind rather than in cash. The total cash funding of the project over its three-year term comprises:

ARC      $232,449 POs$88,412

Total     \$320,861

## PROJECT RESOURCES AND MANAGEMENT

The project is managed by a Steering Committee consisting of six members:

• three academics (the authors and principal researchers); and
• a representative of each of the three POs.

The head count of the project itself, in addition to assistance provided by the POs, is currently seven, consisting of:

• the three principal researchers;
• three students, of which two are enrolled for doctorates and one for an Honours degree; and
• one research assistant.

Although the three students are studying topics that would be acceptable for their degrees in their own right, the topics have been specifically selected to contribute to the claim dependency project. Brief descriptions of their projects are as follows.

### FIRST PHD PROJECT (XINDA YANG)

Aim to construct a micro-level dynamic model that describes the stochastic characteristics of the arrivals and the development patterns of claims from multiple lines of business (LoBs) with dependencies between them.

### SECOND PHD PROJECT (PHUONG ANH VU)

Aim to model aggregate data from multiple LoBs, representing dependencies between them by means of specific multivariate distributions. The models will also be dynamic in the sense of incorporating parameters that evolve over time.

### HONOURS PROJECT (CLEMENT YEUNG)

Aim to construct a superimposed inflation model that incorporates observable predictors beyond those traditionally incorporated in claim reserving models.

## PRELIMINARY WORKSHOP

The project commenced in December 2013, and a workshop was conducted on 18 March 2014, attended by the academic research team and a number of representatives of the POs. The purpose of the workshop was to establish a baseline situation for the project, including:

• current industry approach to the claim dependencies, with special reference to:
– their incorporation in loss reserving and capital modelling;
– the modelling and estimation of them; and
• identification of those aspects of claim dependency currently dealt with well by the industry, and those where further development might be helpful.

## EARLY AVENUES FOR RESEARCH

Beyond the projects pursued by the students under the supervision of the research team, the workshop identified five areas in which immediate research effort was deemed appropriate. Brief detail is given in the following five numbered passages.

### 1. ACCUMULATION OF CORRELATION MATRICES

A number of insurers consider claim dependencies according to a tiered structure. Claims are naturally categorised according to LoB, but then each LoB sub-categorised according to a number of sources of risk, e.g. data quality, judicial inflation, etc.

This results in the need to consider correlation matrices of the form illustrated in Figure 1, which exhibits major and minor divisions of the tiered structure.

These matrices are clearly large, and their construction is not necessarily straightforward. Sometimes an insurer might proceed by defining the diagonal blocks (i.e. correlation matrices for single LoBs), and also the diagonal blocks of an alternative matrix in which the roles of LoB and risk source are interchanged (i.e. correlation matrices for single risk sources).

The challenge is then to complete the rest of the matrix (i.e. elements corresponding to different LoBs as well as different risk sources) in such a way that the completed matrix is positive definite.

### 2. SELECTION OF CORRELATION MATRICES

Insurers often use a process of mapping qualitative scores of dependency to correlation matrices, where the latter contain semi-arbitrary numerical values. This raises the question concerning the positive definiteness of the matrices. It might be possible to consider more structured forms of mapping.

### 3. MERGER OF PEARSON CORRELATION AND TAIL DEPENDENCY

Pearson correlation is often used as a measure of dependency. This may be a suitable measure for observations not too distant from the centre of distributions, but can fail as a measure of dependency of the tails.

The question arises as to how one could account for dependency at medium-high percentiles when using Pearson correlation for mid-range percentiles and tail dependency for high percentiles.

### 4. DEPENDENCY BETWEEN PAST AND FUTURE

It was felt by industry that a better means of this form of dependency might be investigated.

### 5. STRUCTURE OF DEPENDENCY BETWEEN TRIANGLES

Most dependency modelling in the literature is restrictive in the forms of dependency contemplated. Dependency may be assumed, for example, between the same accident years within different LoBs, but independence assumed between different accident years; or between the same payment years within different LoBs, but independence between different payment years; and so on.

There is an evident need to consider more comprehensive dependency structures, but without the introduction of an excessive number of parameters.

Research has commenced in some of these subject areas and is planned for the others in the near future.

## DATA

One of the great in-kind contributions by some of the POs is the provision of extensive data sets. These are to be provided in respect of two short tail and two long tail LoBs, namely:

• Motor;
• Home (Buildings and Contents separately);
• Compulsory Third Party; and
• Public Liability.

Unit record claim data sets will be provided (with insured de-identified), yielding far more information than the traditional claim triangles. Further, each record will contain not only payment and case estimate information, but also various covariates associated with the claim. This will enable the construction of micro-models.

## FUTURE DEVELOPMENTS

At this early stage we have assembled a strong research team, to which we hope to add to with the passage of time. Even without addition, we shall have a team of seven devoting a total of perhaps seven or eight full-time equivalent person-years to an issue of significance to the insurance industry. We are hopeful of a substantial and practical contribution to knowledge.

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