General Insurance Convention 1998

GISG Working Parties

Benchmarking. - Theaker, David N; Upson, James R K; Wrenn, Stuart A. 18 pages.
The aim of the paper is to bring together some of the ideas and issues associated with benchmarking, with particular reference to the insurance industry and the actuarial profession. Areas covered include consideration of the characteristics of benchmarks, the use of benchmarking as a business management tool, and a brief look at benchmarking of financial factors. Finally, there is consideration of benchmarking in the area of professional standards.

Data warehousing. - Bland, Richard H; Cooper, Melanie J; Harris, Simon D; Massey, Roger; Perry, Geoff. 45 pages.
This paper is a discussion of data warehousing with an emphasis on actuarial and business approaches. The main section is an introduction to the concepts of warehousing and its business implications. The benefits and risks are discussed, along with the practical issues of structuring a warehousing project. Some guidelines for a successful warehousing project are suggested. To give some perspective, there is a short appendix with the history of one company's warehousing project.
A further three appendices are provided to give a full technical discussion of the IT issues in warehousing. These cover data models, some examples of these applied to retail and insurance, and a discussion of user tools. A number of warehouse projects fail because of inappropriate choices of data models and user tools. These appendices, although technical, are intended to provide insight into why these failures occur.

Measuring competitiveness simply. - Bradley, Helen L; Chapman, Alastair S; Honiball, Peter; Howard, Sheree K; Levay, Edward J; Mokhtar, Nurnajwa; Morgan, Kathryn A; Verrall, Richard J. 43 pages.

Reserving and pricing for large claims. - Czernuszewicz, Andrzej J; Couper, Andrew J; Orr, James B; Seago, Wendy A; Upson, James R K; Howard, Sheree K; Mitchell, Nicola S; McPherson, James. 46 pages.
The report aims to provide a guide to new actuaries and non-actuaries, and encourage debate amongst experienced actuaries as to the treatment of large claims.

The reserving of non-standard classes of insurance. - Harding, R Justyn; Hindley, David J; Lyons, Graham E; Stock, Richard A. 47 pages.
It is not long since the Institute/Faculty produced the new Claims Reserving Manual. This has two volumes describing a large number of reserving methods. However, most of these methods are for standard classes.
They rely to a considerable extent on various conditions which are presumed to apply such as: Adequate data; Homogeneity of data; Regular development of data; A stable mix of business and types of claim over time; Absence of calendar year effects on development data; No abrupt changes in circumstances (legal, administrative, or otherwise); Past development of data being a reliable indicator of future development; Annual policies; High frequency/low severity.
This paper examines a number of methods which can be used for classes of business, or sub-sections of classes, where some of these conditions do not apply. As the methods are designed to overcome similar problems it is likely that the solution to reserving for any other non-standard class can be found by examination of the various approaches in this Paper.

Securitisation. - Sayers, Jeffery E; Fulcher, Graham. 78 pages.

UK household business. - Jones, Stephen Michael; Williams, Nathan P; Winter, Richard D. 40 pages.

Appendix A : Survey of proprietory risk assessment systems

Year 2000. - Cresswell, Catherine; Czapiewski, Colin J W; Hubbard, Andrew; Slater, David A. 48 pages.
In this paper we aim to investigate the ramifications of the millennium bug for insurance enterprises. We describe, briefly, the millennium and similar date related bugs, their possible business and economic consequences and the time-frame over which the consequences of date related bugs may emerge. We go on to discuss the coverage issues the millennium bug raises and underwriting and reserving issues. In the appendix we consider the possible impact for each major line of business.
The paper focuses principally on UK policy forms, but we imagine similar coverage issues will arise in other jurisdictions.

GISG Workshops

Actuaries in claims management advisory roles [summary only]. - Falcone, Mike; White, Graham. 2 pages.

Customer lifetime value [summary only]. - Brickman, Simon J. 2 pages.

Preparing for the Euro [summary only]. - Taylor, John M. 2 pages.

Price/demand elasticity. - Kelsey, Richard; Anderson, J Duncan; Beauchamp, Richard L; Black, Simon A J; Bland, Richard H; Klauke, Paul; Senator, Ian. 13 pages.
The aim of the workshop will be to discuss the development of a price demand elasticity model and the practical uses of such a model.
There will be presentation of the approach to, and results from a price/demand elasticity modelling investigation based upon an anonymous data pool of direct motor insurance quotation, conversion and renewal data.

Reinsurance bad debt provisions [summary only]. - Bulmer, J Richard (Chairman) 5 pages.

Reinsurance pricing. - Chandaria, Sanjiv (Chairman). 28 pages.

Standard errors of prediction in claims reserving: a comparison of methods. Analytic and bootstrap estimates of prediction errors in claims reserving. - England, Peter D; Verrall, Richard J. 20 pages.
Renshaw and Verrall (1994) have suggested a stochastic claims reserving model which reproduces the reserve estimates provided by the standard chain ladder model (subject to constraints on the pattern of negative incremental claims). Their model falls within the generalised linear modelling (GLM) framework and can be fitted easily using standard statistical software packages. Having fitted the model, it is possible to obtain analytic prediction errors of the reserves. The GLM framework suggests appropriate goodness-of-fit measures, and also gives a choice of appropriate residual definitions which can be used for informal diagnostic checks of the fitted model. Residuals can also be used in a bootstrap exercise providing a computationally simple method of obtaining estimates of the reserve prediction errors. In this paper, we consider an appropriate residual definition for this purpose, and show how the bootstrap prediction errors can be computed easily in a spreadsheet, without the need for statistical software packages. The bootstrap prediction errors are compared with their analytic equivalent, and also compared with other methods commonly used, including Mack's distribution free approach (Mack 1993) and methods based on log-linear models.

The transitional state chain-ladder method. - Lovick, Anthony C. 9 pages.
The purpose of this method is to offer the Reserving Actuary an alternative in cases where the Paid and the Incurred chain-ladder methods both fail to produce valid results.
Based on the Chain-ladder this method gives an alteration which allows the separation of claims which Settle, from those that remain Outstanding, at each development period.

Papers submitted for the Brian Hey Prize

Financial pricing of insurance in the multiple line insurance company. - Cummins, J David; Franklin, Allen; Phillips, Richard D. 51 pages.
This paper uses a contingent claims framework to develop a financial pricing model of insurance that overcomes one of the main shortcomings of previous models - the inability to price insurance by line in a multiple line insurer subject to default risk. The model predicts that prices will vary across firms depending upon firm default risk, but within a given insurer prices should not vary after controlling for line-specific liability growth rates. We also analyze an important qualification to this result for insurance groups, where several insurer subsidiaries are owned by a primary insurer or holding company. Because the owners of the group have the option to allow individual subsidiaries to fail, insurance groups with assets and liabilities widely dispersed among subsidiaries are predicted to command lower prices than otherwise identical insurers where assets and liabilities are concentrated in one or a few corporate entities. Empirical tests using data on publicly traded property-liability insurers support the hypotheses: prices vary across firms depending upon overall- firm default risk and the concentration of business among subsidiaries; but within a given firm, prices do not vary by line after adjusting for line-specific liability growth rates.

Pricing for risk in financial transactions. - Christofides, Stavros. 47 pages.
This paper considers the pricing of uncertain cash flows, which includes those arising in insurance and reinsurance, using the proportional hazards (p-h) transform pricing basis defined by Wang (1995). This basis satisfies all the desirable properties of a sound pricing principle including sub- additivity and layer additivity and is a generalisation of the classic Standard Deviation Principle of Risk Theory, which appears to be valid when the underlying distribution has fixed skewness. The p-h basis deals with all distributions, including empirical ones, by taking account of all their moments in its formulation.

Pricing of insurance risk. - Mehta, Shyam J B. 36 pages.
This paper develops an approach and presents some evidence as to the pricing of life and property/casualty reinsurance treaties allowing for risk. A key aspect of the study was to see whether the empirical and theoretical findings of modem financial theory apply to reinsurance pricing.

ASTIN papers

Asset modelling - empirical tests of yield curve generators. - Venter, Gary G. 15 pages.
Some empirical tests for stochastic yield curve generators are proposed. The basis of the tests is to compare history to the model for the conditional distributions of various yield-curve statistics given the three-month rate. The term structure of US Treasury instruments will be used as an example.

Currency risk models in insurance: a mathematical perspective. - Cox, Samuel H; Pedersen, Hal W. 36 pages.
In this paper we consider a general two-country model of exchange rate dynamics in which interest rates are stochastic. Special cases of this model are also illustrated in which the interest rates are constant in each country and when interest rates are Gaussian in each country. Uncertainty in this global economy consists of the exchange rate between the two countries and the noise in interest rates in each local economy. This model provides an important tool for actuaries dealing with global risk which includes valuation of currency derivatives (forwards, futures, options and swaps), frequency/severity claims model with exchange rate risk in the claim size (i.e. the claims are paid in a foreign currency), valuation of individual insurance contracts written in foreign currency, and valuation of general interest sensitive claims in foreign currency. Typical examples of practical importance include marine insurance, health insurance, and life insurance. The simple case of the model for which interest rates are constant in each local economy is used to explain and analyse the "Siegel paradox" [32] (or lack thereof) which we describe because it has confused some readers of the 1970 era currency risk literature. We illustrate the model with the calculation of forward prices, currency options, a simple life insurance contract, and a marine insurance policy.

Dynamic dynamic-programming solutions for the portfolio of risky assets. - Tenney, Mark S. 14 pages.
Dynamic programming solutions for optimal portfolios in which the solution for the portfolio vector of risky assets is constant were solved by Merton in continuous time and by Hakansson and others in discrete time. There is no case with a closed form solution where this vector of risky asset holdings changes dynamically. This paper derives such solutions for the first time, and is thus a dynamic dynamic-programming solution as opposed to a static dynamic-programming solution for this vector. The solution is valid when there is a set of basis assets whose excess expected return is linear in the state vector, whose variance-covariance matrix is time- dependent and for which the interest rate is a quadratic function of the state vector.

Extreme value techniques. Part I - pricing high-excess property and casualty layers. - List, Hans-Fredo; Zilch, Rita. 28 pages.
We show how modem extreme value theory concepts for the estimation of longtailed loss severity distributions and simulation approaches to parameter uncertainty and aggregate loss calculations can be used to create a family of new multiline, multiyear risk transfer products for the Fortune 500 group of large industrial companies. Swiss Re's recently launched 'Beta' high- excess property and liability coverage for the Oil & Petrochemicals industry is presented as an example for a successful application of this methodology.

Extreme value techniques. Part II - value proposition for Fortune 500 companies. - Geosits, Gerhard; List, Hans-Fredo; Lohner, Nora. 29 pages.
Swiss Re's Value Proposition is basically a consulting approach in which [using Swiss Re's risk-adjusted capital (RAC) concept] an optimal self-insured retention (SIR) is determined for a particular insured. Very early on in the 'Beta' product engineering process (described in Extreme Value Techniques - Part I), the 'Beta' implementation team made sure that: (1) 'Beta' standard coverages implement Swiss Re's Value Proposition for 'catastrophic' (or 'Beta') events and (2) that the 'Beta' pricing process fully reflects Swiss Re's Value Proposition for corporate clients in the Fortune 500 group of companies. This paper describes the 'Beta' (extreme value theory) implementation of Swiss Re's Value Proposition. The Oil & Petrochemicals industry is used as an example.

Extreme value techniques. Part III - increased limits factors (ILF) pricing. - List, Hans-Fredo; Lohner, Nora. 39 pages.
In order to further simplify the 'Beta' pricing approach (described in Extreme Value Techniques - Part I and Part II), an alternative to existing increased limits factors (ILF) rating methodologies (see eg, Loss Distributions, Hogg and Klugman, Wiley 1984) is developed in this short note, together with a corresponding pricing tool, the main objective being to make such a new ILF tool consistent with the 'Beta' extreme value theory approach to risk quantification while maintaining much of the simplicity of the existing ILF methodologies. The Oil & Petrochemicals industry is used as an example.

Extreme value techniques. Part IV - fin re pricing. - Buhlmann, Niklaus; Bochicchio, Vincenzo; Junod, Stephane. 63 pages.
We present a state-of-the-art rating methodology for financial reinsurance contracts that is based upon a consistent stochastic model (of the jump diffusion type) for financial market variables (like, eg, interest rates, foreign currencies, stocks, stock indices, etc.) as well as for (excess-of-loss) reinsurance claims. A lattice-based implementation of this pricing methodology (ie, a corresponding Fin Re Toolbox) is discussed in some detail and then applied to rate current example Fin Re contracts taken from the Swiss Re New Markets business area.

The handling of continuous tariff variables: tips and experiences. - Schmitter, Hans; Toniolo, Dino. 10 pages.
Using continuous variables to describe some data we often Incur in some plausibility problems for extreme low and high values. Assuming that the continuous function which describes the relationship between some explanatory variables (covariates) and a response variable lies in a affine linear space (as in the case of the generalised linear models) we can solve these problems with an appropriate choice of the affine linear space.

The impact of proportional mortality profit distribution on solidarity. - Spreeuw, Jaap. 18 pages.
For a given period, a portfolio of individual life contracts to which the same amount at risk applies, will be considered. The portfolio consists of two homogeneous subgroups mutually different with respect to the mortality rate. At the end of the period, a fixed proportion of the mortality result realized by the insurer will be shared equally among the survivors. At the beginning of the period considered, all individuals pay the same average risk premium, while the insurer's aim is to achieve equivalence on the level of the entire portfolio. In this paper it will be investigated how the mentioned proportion affects the absolute and relative subsidizing solidarity.

Largest claims reinsurance premiums under possible claims dependence. - Kremer, Erhard. 15 pages.
Largest claims reinsurance covers are reconsidered. A general new net premium bound is derived and specialized to the situation of Pareto-distributed claims sizes. Important is that the classical assumption of claims-size-independence is not basically assumed, the claims-sizes are allowed to be dependent. No assumptions on the dependence-structure are needed. In an example it is shown for the classical largest claims reinsurance cover that the new bound is quite useful.
Closing the note something is said also on the ECOMOR-treaty.

Liability modelling - empirical tests of loss emergence generators. - Venter, Gary G. 23 pages.
Historical loss reserve analysis focused on reserving techniques. More recently the emphasis is on identifying and parameterizing models of the reserve emergence process. Another application of a reserve emergence model is to use it to simulate realizations of the reserving process for dynamical financial analysis. This paper introduces a classification system for reserve emergence models and addresses empirical tests for identifying the appropriate model for the data at hand.

Minimum solvency margin of a general insurance company: proposals and curiosities. - Bosi, Gianni; Daris, Roberto. 10 pages.
An analytical model is presented for the determination of the minimum solvency margin of a general insurance company. The technical risk proportional to the standard deviation of the aggregate claim amount and the financial risk represented by a multiplying factor are both considered. Further, the ruin probability criterion and the zero expected utility approach starting from a simple solvency condition are compared.

Non-homogeneous Markov and semi-Markov models for pricing derivative securities. - Janssen, Jacques; Manca, Raimondo; Di Biase, Guiseppe. 23 pages.
In this paper for the first time (as far as the authors know) an application of the non- homogeneous Markov and semi-Markov processes aimed at pricing derivative securities has been proposed. The consideration of the nonhomogeneity in the framework of the pricing derivative securities allows us to take into account also the possibility to differentiate the financial operations according to the starting time.

Portfolio optimisation. - Schnieper, Rene. 49 pages.
Based on the profit and loss account of an insurance company we derive a probabilistic model for the financial result of the company, thereby both assets and liabilities are marked to market. We thus focus on the economic value of the company.
We first analyse the underwriting risk of the company. The maximization of the risk return ratio of the company is derived as optimality criterion. It is shown how the risk return ratio of heterogeneous portfolios or of catastrophe exposed portfolios can be dramatically improved through reinsurance. The improvement of the risk return ratio through portfolio diversification is also analysed.

Pricing the risk of a general insurance portfolio using series expansions for the finite time multivariate ruin probability in a financial-actuarial risk process. - Usabel, Miguel A. 20 pages.
The risk involved in a General Insurance portfolio can be priced using the related concepts Multivariate Ruin Probability-Annual Premium. In the present work, McLaurin expansion, with respect the arrival intensity of claims, for the finite time Multivariate Ruin Probability - considering the surplus just before and deficit at ruin time - is obtained in the context of a Financial-actuarial model for the risk process, and used to price a General Insurance portfolio in terms of its annual premium. Finally, the concept of Financial Autonomy Ratio, is introduced as a measure of the strength of the investments' yields to prevent ruin.

Some applications of unsupervised neural networks in rate making procedure. - Pelessoni, Renato; Picech, Liviana. 19 pages.
In recent years, neural networks have been having a wide range of applications. In particular, the unsupervised neural networks are designed to implement clustering techniques. In this paper we apply a two-stage Kohonen Self- Organising Map to collect the basic classes of one tariff variable in clusters. In this procedure we take advantage of the topology preservation property of the Self-Organising Maps in order to build tariff classes containing contiguous values of the tariff variable.

Some estimates on the standard deviation of ultimate claims when judgement is used. - Leifer, Andrew R; Sanders, David E A. 17 pages.
Stochastic control has been used in insurance for some time for peculiar problems. In this paper we shall consider continuous time problems which lead to Hamilton-Jacobi-Bellman equations. These are problems of optimal choice of new business, and of optimal proportional reinsurance. Our objective function will be infinite time ruin probability (which is chosen for simplicity and for the purpose of illustration). Other objective functions (based on utility functions or on expected discounted dividend) are possible and can be treated with essentially the same methods.

Some stochastic control problems in insurance. - Hipp, Christian. 14 pages.

Stochastic claims inflation in IBNR. - Kremer, Erhard. 17 pages.

This paper deals with loss reserving under inclusion of stochastic claims inflation, a topic that is of current interest. Note that recently a new paper on it was presented at the international Astin colloquium at Cairns. In the following it is basically assumed that the discounted claims increase follows an autoregressive model of ARCH-type and that the stochastic yearly interest intensity follows a classical autoregressive model. A procedure to estimate adequately the stochastic discounting factors is deduced. This is combined with the link-ratio technique and the classical forecasting procedure for autoregressive processes, giving a new stochastic loss reserving technique. The whole method is perfect and bandy. Its practicability is demonstrated in an example.

A stochastic model to determine IBNR reserves. - Waszink, Hans; van der Wardt, Michiel. 26 pages.
This paper describes a stochastic model to determine IBNR-reserves based on a Compound Poisson distribution. The number of insureds per accident year and the mean and second moment of payments by accident, reporting and development year are used as input. The claim frequency is estimated by accident and reporting year and the equality of the claim frequencies is tested using a x2 goodness-of-fit test. Mean and second moment of the total claim amount are estimated as the sum of payments in development years starting with the reporting year. After that, the model is applied to a fictitious dataset and the arising difficulties are discussed. It is shown that without testing the equality of claim frequencies, the calculated reserve may lead to an underestimation of future liabilities.

Strong stop-loss criteria: definition and application to risk management. - Deelstra, Griselda; Grasselli, Martino; Koehl, Pierre-Francois. 17 pages.
this paper, we define the concept of strong stop-loss domination and we use it for the obtention of bounds on the hedging price of random variables. These hedging prices depend on the characteristics of the agent and in particular on her utility function, which in hard to estimate in practice. Our bounds have the advantage that they only depend on the characteristics of the financial market and of the random variable to hedge. Moreover, our interval is proved to be coherent with the equilibrium and it is tighter than the one obtained by the classical superreplication approach. At last, specifying the distribution of the financial assets' prices and the random variable to hedge, we compute the upper bound given by the strong stoploss approach and we compare it with the superreplication bound.

Supermodular ordering and stochastic annuities. - Dhaene, Jan; Goovaerts, Marc J. 14 pages.
In this paper, we consider several types of stochastic annuities, for which an explicit expression for the distribution function is not available. We will construct a random variable with the same mean and which is larger in stop- loss order, for which the distribution function can be obtained easily.

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