Solvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

This paper looks at the problems of assessing, for solvency purposes, the capital requirements of a non-life insurer in the context of the United Kingdom. It considers how these capital requirements might vary according to the different risks to which an insurer is subject and how this Risk-Based Capital (RBC) might be measured in practice, using as a case study the RBC formula recently introduced in the United States of America. The paper also discusses the application of RBC concepts to the problem of internal capital allocation, to assist in measuring an insurer's rate of return to shareholders by business unit, as well as the more obvious regulatory application. The advantages and disadvantages of a formula-based approach to capital requirements for solvency purposes are discussed in comparison with possible alternative approaches to insurance supervision.

This paper describes current asset share techniques, examines alternative asset share philosophies and discusses practical issues associated with the calculations. Alternative approaches to smoothing payouts using asset shares are examined. A financial management framework is described which provides information on the financial position of a with-profits fund. A central part of the framework is the concept of risk-based capital. The factors to be considered in determining risk-based capital are described and examples given of the possible capital needs of with-profits business.

A project to develop an Accounting Standard for Insurance, with the aim of enhancing understandability, relevance, reliability and comparability of general purpose financial reporting for insurance worldwide, is being progressed by the International Accounting Standards Board. The basis of the proposals is that assets and liabilities be shown at fair values (market values for quoted instruments). This paper, prepared by a Working Party established by the Life Board of the United Kingdom actuarial profession, summarises and comments upon a number of the principal features of the proposals, as they have emerged up to September 2001. The paper goes on to consider how a system of reporting for prudential regulatory purposes might be built upon a fair value general reporting base, summarising the thinking of a number of other bodies, proposing certain principles and suggesting lines of development. The appendices to the paper discuss a number of issues in further depth and present some illustrative results of some investigations into applying fair value methods in practice. The emphasis of the paper is on reporting for life assurance business, although many of the principles apply equally to general insurance.

The approaches to liability valuation, assessment of prudential capital and measurement of profit for life offices are undergoing radical change. A common thread runs through all of these proposed changes — each change represents a move away from traditional actuarial approaches towards a more economically coherent, market-consistent approach. These changes should encourage a general improvement in the life industry's risk management processes. However, they will come at a cost. The measurement of the economic risks generated by the complex guarantees written by life offices is far more difficult than applying the latest resilience test equity fall. This will require a step change in the sophistication of life offices' risk and capital measurement and management know-how. The measurement of value, risk and capital will soon demand the application of ‘stochastic’ modelling tools. In this paper, we explore some of the issues raised by the application of these approaches to the valuation and risk management of with-profits business.

We revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.