# Gregory Clive TaylorUNSW Sydney | UNSW · School of Risk & Actuarial Studies

Gregory Clive Taylor

Officer of the Order of Australia (AO), BA, PhD, PhD Macquarie | FIA, UK | FIAA, Australia | FIMA

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181

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## Publications

Publications (181)

High-cardinality categorical features are pervasive in actuarial data (e.g., occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings.
In this work, we present a novel Generalised Linear Mixed Model Neural Network (“GLMMNet”) approach to the modelling of high-cardinal...

The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a...

Traditional techniques for calculating outstanding claim liabilities such as the chain-ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck & Debruyne (2011, Insurance: Mathematics and Economics , 48 , 85–98)...

The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced...

High-cardinality categorical features are pervasive in actuarial data (e.g. occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings. In this work, we present a novel _Generalised Linear Mixed Model Neural Network_ ("GLMMNet") approach to the modelling of high-cardina...

This paper is concerned with modelling multiple claim arrays that are subject to one or more common shocks. It uses a structure that involves very general forms both idiosyncratic and common shock components of cell means. The dependencies between arrays, or between cells within an array, generated by the shocks are also of very general form. All o...

In this paper, we first introduce a simulator of cases estimates of incurred losses called SPLICE ( S ynthetic P aid L oss and I ncurred C ost E xperience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the l...

Traditional techniques for calculating outstanding claim liabilities such as the chain ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck and Debruyne (2011) and Verdonck and Van Wouwe (2011). In this paper...

In recent years, new techniques based on artificial intelligence and machine learning in particular have been making a revolution in the work of actuaries, including in loss reserving. A particularly promising technique is that of neural networks, which have been shown to offer a versatile, flexible and accurate approach to loss reserving. However,...

The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a...

The paper is concerned with common shock models of claim triangles. These are usually constructed as a linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduc...

In this paper, we first introduce a simulator of cases estimates of incurred losses, called `SPLICE` (Synthetic Paid Loss and Incurred Cost Experience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the lifet...

Neural networks offer a versatile, flexible and accurate approach to loss reserving. However, such applications have focused primarily on the (important) problem of fitting accurate central estimates of the outstanding claims. In practice, properties regarding the variability of outstanding claims are equally important (e.g., quantiles for regulato...

The paper is concerned with a particular sub-family of the Tweedie family of distributions characterized by a constant mean-to-variance ratio (“CMVR”). The properties of the CMVR sub-family are explored. Some of these, concerned with addition of CMVR variates, are well adapted to the treatment of insurance losses and loss reserves. The tricky issue...

Recent years have seen rapid increase in the application of machine learning to insurance loss reserving. They yield most value when applied to large data sets, such as individual claims, or large claim triangles. In short, they are likely to be useful in the analysis of any data set whose volume is sufficient to obscure a naked-eye view of its fea...

In this paper, we develop a method to model and estimate several, dependent count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims). The dependency structure is introduced via multivariate shot noise intensity process...

A simulator of individual claim experience called SynthETIC is described. It is publicly available, open source and fills a gap in the non-life actuarial toolkit. It simulates, for each claim, occurrence, notification, the timing and magnitude of individual partial payments, and closure. Inflation, including (optionally) superimposed inflation, is...

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, com...

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of...

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, com...

In this paper, we focus on estimating ultimate claim counts in multiple insurance processes and thus extend the associated literature of micro-level stochastic reserving models to the multivariate context. Specifically, we develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business. The de...

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are al...

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are al...

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of...

It is probably fair to date loss reserving by means of claim modelling from the late 1960s [...]

The purpose of this paper is to survey recent developments in granular models and machine learning models for loss reserving, and to compare the two families with a view to assessment of their potential for future development. This is best understood against the context of the evolution of these models from their predecessors, and the early section...

The defining feature of the Cape Cod algorithm in current literature is its assumption of a constant loss ratio over accident periods. This is a highly simplifying assumption relative to the chain ladder model which, in effect, allows loss ratio to vary freely over accident period.
Much of the literature on Cape Cod reserving treats it as essential...

The paper is concerned with multiple claim arrays. In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, we develop a methodology for the construction of such correlation structures (to any dimension). Indeed, the literature does not document any metho...

This is a practical paper, concerned with certain existing industry practices used to factor large correlation matrices into estimates of variance of total portfolio liabilities, and hence into risk, and possibly capital margins, and the extent to which those practices are theoretically sound. Two such practices are examined, and the results of thi...

The hierarchical credibility model was introduced, and extended, in the 70s and early 80s. It deals with the estimation of parameters that characterize the nodes of a tree structure. That model is limited, however, by the fact that its parameters are assumed fixed over time. This causes the model's parameter estimates to track the parameters poorly...

The cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesia...

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer’s portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach...

The paper is concerned with multiple claim arrays. We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles a...

This paper is concerned with dependency between business segments in the Property & Casualty industry. When considering the business of an insurance company at the aggregate level, dependence structures can have a major impact in several areas of Enterprise Risk Management, such as in claims reserving and capital modelling. The accurate estimation...

The literature on Bayesian chain ladder models is surveyed. Both Mack and cross-classified forms of the chain ladder are considered. Both cases are examined in the context of error terms distributed according to a member of the exponential dispersion family. Tweedie and over-dispersed Poisson errors follow as special cases. Bayesian cross-classifie...

The purpose of the present paper has been to test whether loss reserving models that rely on claim count data can produce better forecasts than the chain ladder model (which does not rely on counts); better in the sense of being subject to a lesser prediction error.
The question at issue has been tested empirically by reference to the Meyers-Shi d...

SOME years ago G. F. Hardy proposed a method of performing a mortality graduation in accordance with Makeham's formula. This method is now well known to actuaries of the British tradition, having been absorbed into textbooks some time ago. A less known method of performing such a graduation was suggested by Cram6r and Wold in 1935. The two methods...

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer’s portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach...

One of the most powerful devices in the theory of compound interest is Makeham's formula. The essence of the formula may be stated as follows:
Consider an admitted loan of C bearing interest at rate g per annum (payable pthly in arrear) per unit of admitted capital. The loan is to be repaid by a series of payments each of which contains a capital p...

By claims experience monitoring is meant the systematic comparison of the forecasts from a claims model with claims experience as it emerges subsequently. In the event that the stochastic properties of the forecasts are known, the comparison can be represented as a collection of probabilistic statements. This is stochastic monitoring. This paper de...

The chain ladder is considered in relation to certain recursive and non-recursive models of claim observations. The recursive models resemble the (distribution free) Mack model but are augmented with distributional assumptions. The non-recursive models are generalisations of Poisson cross-classified structure for which the chain ladder is known to...

It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised lin...

This paper examines various forms of individual claim model for the purpose of loss reserving, with emphasis on the prediction error associated with the reserve. Each form of model is calibrated against a single extensive data set, and then used to generate a forecast of loss reserve and an estimate of its prediction error.
The basis of this is a m...

This paper constructs and studies a simple but realistic model of an insurance market. The model has a minimalist construction in the sense that the number of parameters defining it is strictly limited and the elimination of any one of them would destroy its realism. There are 11 es- sential parameters. Each of the parameters has a physical interpr...

This paper investigates the practical aspects of applying the second-order Bayesian revision of a GLM to form an adaptive filter for claims reserving. It discusses the application of such methods to three typical models used in Australian general insurance circles. Extensions, including the application of bootstrapping to an adaptive filter and the...

It has been known since Zehnwirth (1977) that a scalar credibility coefficient is closely related to the F-statistic of an analysis of variance between and within risk clauses. The F-statistic may also be viewed as testing a certain regression structure, associated with credibility framework, against the null hypothesis of a simpler structure.
This...

In this article we consider the situation in which an insurer requires a loss reserve, together with the estimated prediction error, in respect of a number of stochastically dependent lines of business, individually and in aggregate. We suppose that generalized linear models are used to estimate each of the individual loss reserves, and that bootst...

It has been known since Zehnwirth (1977) that a scalar credibility coefficient is closely related to the F-statistic of an analysis of variance between and within risk clauses. The F-statistic may also be viewed as testing a certain regression structure, associated with credibility framework, against the null hypothesis of a simpler structure.
This...

The following items of terminology are equivalent: non‐life insurance, property–liability insurance, property and casualty insurance, and general insurance.
Non‐Life insurance is defined and distinguished from other forms of insurance. Classes of non‐life insurance are defined and discussed. Reinsurance is also defined.

This article discusses the circumstances under which a claim will be paid by an insurance policy and some basic matters affecting the amount of claim payable. Various pieces of terminology are defined.

Synchronous bootstrapping of seemingly unrelated regressions 1 Summary Consider the seemingly unrelated regression framework, in which regression models are applied to a number of data sets, with stochastic dependencies between them. The regression models are not restricted to general linear models (e.g. GLMs). Forecasts are required, with estimate...

The author places the discounting of loss reserves for investment income within a financial economics context. This enables the evaluation of a loss reserve containing a security margin, such as to produce p% confidence in adequacy, taking account of both asset and liability risks. This loss reserve is expressed as a multiple of the economic value...

The chain ladder forecast of outstanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiase...

The chain ladder forecast of outstanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiase...

The paper reviews the development of loss reserving models over the past, classifying them according to an elementary taxonomy. The taxonomic components include (1) the algebraic structure of the model, (2) the form of its parameter estimation, (3) whether or not it is explicitly stochastic, and (4) whether or not its parameters evolve over time. P...

This paper is concerned with funding systems, i.e. systems which accumulate funds for the future payment of financial obligations. Commonly, such funding requires a balance between (1) the desire to minimise the contributions that need to be diverted from other use to the support of the Fund, and (2) the need to maintain reasonable solvency in the...

The paper is concerned with loss reserving at the individual claim level (also referred to as micro-reserving or granular reserving) in the context of workers compensation, or similar income replacement insurance. The individual claim reserve is constructed on the basis of detailed information, specific to the claimant and the circumstances of the...

Whittaker graduation is applied to the spatial smoothing of insurance data. Such data (e.g. claim frequency) form a surface over the 2-dimensional geographic domain to which they relate. Observations on this surface are subject to sampling error. They need to be smoothed spatially if a reliable estimate of the underlying surface is to be obtained....

All property and casualty insurers are required to carry out loss reserving as a statutory accounting function. Thus, loss reserving is an essential sphere of activity, and one with its own specialized body of knowledge. While few books have been devoted to the topic, the amount of published research literature on loss reserving has almost doubled...

The operation of a bonus-malus system, superimposed on a premium system involving a number of other rating variables, is considered. To the extent that good risks are rewarded in their base premiums, through the other rating variables, the size of the bonus they require for equity is reduced. This issue is discussed quantitatively, and a numerical...

Consider an excess-of-loss reinsurance arranged in a number of layers. A loss reserve is required for each layer. There are two major reasons why the independent application of some conventional loss reserving technique to each layer is inappropriate. First, the experiences in different layers in respect of a particular treaty year will be linked;...

This article is concerned with insurer capitalization and its implications for insurance pricing. It establishes an economy-wide one-period model of the dependencies between the prices of insurance and other stocks, real assets, and insurance policies, as well as consumer preferences for consumption relative to saving and insurance security, and in...

This article considers several well known methods of calculating fair premium rates. Particular reference is made to the Myers-Cohn and internal rate of return methods. In the absence of taxes, the most natural application of each method produces a return on equity, period by period, which is consistent with the capital asset pricing model. Hence,...

Mortgage insurance indemnifies a mortage lender against loss on default by the borrower. The sequence of events leading to a claim under this type of insurance is relatively complex, depending not only on the credit worthiness of the borrower but also on a number of external economic factors.
Prominent among these external factors are the loan to v...

The incidence of risk under a credit insurance policy depends on the original term of the policy and the policy duration at which the incidence of risk is considered. Section 3 of the paper describes the procedure used to fit a bivariate function to this incidence. Section 4 gives the numerical detail of this model. Section 5 makes a comparison of...

The primary purpose of the paper is to place Whittaker—Henderson graduation in a Bayesian context and show that this determines in a precise manner the extent to which goodness-of-fit should be traded off against smoothness in the Whittaker—Henderson loss function. This is done in Section 2.Section 3 generalizes the set of admissible graduating fun...

Taylor G. Risk exchange II: optimal reinsurance contracts. Scand. Actuarial J. 1992; 1: 40-59. The paper, a sequel to Taylor (1992), discusses risk exchange (REX) and reinsurance. A REX is global if its recoveries depend on just aggregate claims of the insurer in question; local if it depends on individual claims. A reinsurance is a 2-party REX und...

The paper unifies certain concepts which have arisen within the field of risk exchange. Borch's theorem on Pareto-optimal risk exchanges is shown to be derivable from a Bowley solution when there are only two participants in the risk exchange. This theorem is then extended to an n-party risk exchange by equating this to a sequence of 2-party exchan...

It is the conventional wisdom of the insurance industry the world over that the industry is subject to an underwriting cycle. By this is meant that the industry’s profit exhibits cyclical behaviour over time. In this context “profit” usually means total operating profit rather than just the underwriting profit component, though in the present paper...

The paper gives details of a case study in the premium rating of a Householders Contents insurance portfolio. The rating is performed by the fitting of bivariate spline functions to a version of operating ratio described in Section 3.
The use of bivariate splines requires a small amount of mathematical equipment, which is developed in Section 4. Th...

An insurer is solvent if it has sufficient assets to meet its liabilities.

The paper considers systems of payments which are not fully funded, i.e partially funded or fully unfunded. Generally, the objective is to be able to establish a premium formula which is consistent with long term planning as to e.g. a target rate of funding, limited variation in premiums from year to year, etc. The premium formulas considered are t...

The paper considers the benefits to be gained from diversification of an insurance operation into a number of classes of business. This is formulated mathematically. It is assumed that the insurer's objective is to maximize increase in utility of wealth over the period up to his planning horizon (Section 2).Several forms of solution of this problem...

The principle of zero utility in premium rating is examined in case of non-exponential utility.