This paper shows how the powerful and flexible tool of stochastic modelling can be applied to a range of business decisions extending far beyond the asset allocation solutions that are common to many asset/liability modelling studies. The example used to demonstrate these techniques is a general insurance case study, but similar principles can be extended to many different business situations. At each stage of the analysis we consider the implications of modern financial theory on the management decision process together with a practical perspective on observed behaviour in the real world. Opportunities are taken to suggest directions in which further research may be of benefit to the actuarial profession.

This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.

Dynamic financial analysis (DFA) is a technique which uses Monte Carlo simulation to investigate the evolution over time of financial models of funds, complex liabilities and entire firms. Although of increasing popularity, the drawback of DFA is the dearth of systematic methods for optimising model parameters for strategic financial planning. This paper introduces strategic DFA which employs the only recently mature technology of dynamic stochastic optimisation to fill this gap. The new approach is described in terms of an illustrative case study of a joint university/industry project to create a decision support system for strategic asset liability management involving global asset classes and defined contribution pension plans. Although the application of the system described in the paper is to fund design and risk management, the approach and techniques described here are much more broadly applicable to strategic financial planning problems; for example, to insurance and reinsurance firms, to risk capital allocation in financial institutions and trading firms and to corporate investment and business development involving real options. As well as describing the mathematical and statistical models used in the case study, the paper treats econometric estimation, asset return and liability scenario generation, model specification and optimisation, system evaluation and historical backtesting. Throughout the system visualisation plays an important role.

Dynamic financial analysis has become one of the important tools that actuaries use to model the underwriting and investment operations of insurance companies. The first step in carrying out the analysis is to investigate the most important factors affecting company performance. This paper identifies the determinants of the performance of United Kingdom general insurance companies using a panel data set consisting of economic data and Financial Services Authority/Department of Trade and Industry returns over the period 1986 to 1999. Three performance measures are used to capture different aspects of insurance operations. These measures are related to a number of economic and firm specific variables, chosen on the basis of relevant theory and literature. An ordinary least squares regression model and two panel data models are estimated for each of three performance measures. This paper also addresses several important econometric problems that are usually ignored in applied work in the context of panel data analysis. Based on the empirical results, this study finds that liquidity, unexpected inflation, interest rate level and underwriting profits are statistically significant determinants of the performance of U.K. general insurers.

This paper extends the methods introduced in England & Verrall (2002), and shows how predictive distributions of outstanding liabilities in general insurance can be obtained using bootstrap or Bayesian techniques for clearly defined statistical models. A general procedure for bootstrapping is described, by extending the methods introduced in England & Verrall (1999), England (2002) and Pinheiro et al. (2003). The analogous Bayesian estimation procedure is implemented using Markov-chain Monte Carlo methods, where the models are constructed as Bayesian generalised linear models using the approach described by Dellaportas & Smith (1993). In particular, this paper describes a way of obtaining a predictive distribution from recursive claims reserving models, including the well known model introduced by Mack (1993). Mack's model is useful, since it can be used with data sets which exhibit negative incremental amounts. The techniques are illustrated with examples, and the resulting predictive distributions from both the bootstrap and Bayesian methods are compared.

This paper presents the findings of a survey of the current Dynamic Financial Analysis (DFA)/Financial Condition Report (FCR) practices in the United Kingdom general insurance industry. An independent samples t test for non-respondent bias was conducted, and the results suggest that the respondent sample is representative of the survey population. The survey results revealed: (1) that the use of DFA techniques in the industry was limited; (2) that scenario testing was the most frequently used technique; (3) that the most common DFA application was the evaluation of reinsurance programmes; (4) that less than ten scenarios were run regularly; (5) that inflation was the most frequently modelled economic variable; (6) that the capability of asset modelling of general insurers was restricted; (7) that the most common method of liability modelling was to use all in force policies in aggregate; (8) that the most common projection periods in DFA and business planning were three years; (9) that the main reason for not using DFA techniques and producing FCR was lack of need; and (10) that views on whether a Guidance Note on FCR specifically for general insurers should be introduced differed.

We tackle problems that appear in the practical application of the Mack method for the estimation of reserving risk and the bootstrapping of ultimate reserve distributions. More specifically, we design a filter for outliers and large jumps, and present a robust version of Mack's variance estimator. A combination of these guarantees a reasonable Mack and bootstrap error even for deficient data. Furthermore, a method is derived that allows us to remove the influence of fluctuations in earning patterns from the reserve risk estimate. It is thereby shown that the relation between underwriting and accident year based loss development patterns is given by a convolution. A numerically stable inversion thereof is obtained by means of a Tikhonov regularization. The reliability of the presented methods is verified with several loss triangles.

In the last few years we have witnessed growing interest in Dynamic Financial Analysis (DFA) in the nonlife insurance industry. DFA combines many economic and mathematical concepts and methods. It is almost impossible to identify and describe a unique DFA methodology. There are some DFA software products for nonlife companies available in the market, each of them relying on its own approach to DFA. Our goal is to give an introduction into this field by presenting a model framework comprising those components many DFA models have in common. By explicit reference to mathematical language we introduce an up-and-running model that can easily be implemented and adjusted to individual needs. An application of this model is presented as well.

This paper describes the dynamic financial analysis model currently being used by a property catastrophe reinsurer to manage its business. The model is-an integral part of the day-to-day operations at the Company, and is used as a decision making tool in the underwriting, investment, and capital management processes. The paper begins by describing the framework that the Company uses for risk management. This includes a classification of the risks facing the Company, which is used to define and prioritize their implementation in the model. Also included is a description of the conceptual approach the Company takes to evaluate the tradeoff between risk and return. The paper then goes on to describe the structure and operation of the dynamic financial analysis model and provides examples of its use at the Company, along with illustrative examples of the various types of output it produces.