Preliminary Announcement

Workshop on

The Interface Between Quantitative Finance and Insurance

4-8 April, 2005

Heriot-Watt University, Edinburgh

A satellite workshop of the Quantitative Finance programme of the Isaac Newton Institute,

January - June 2005,

And

A 2005 Regional Seminar of the AFIR Section of the International Actuarial Association.

Organised jointly by:

Heriot-Watt University, Edinburgh

The International Centre for Mathematical Sciences, Edinburgh

The Isaac Newton Institute, Cambridge

Organising Committee:

Andrew Cairns (Heriot-Watt University),

Claudia Klueppelberg (Technical University of Munich),

Susan Pitts, Chris Rogers (University of Cambridge)

Workshop Summary

This workshop aims to discuss leading-edge research on the interface between insurance, pensions and quantitative finance. It is intended that the meeting will concentrate on two closely linked themes. First, all insurance companies and pension plans are subject to a degree of financial and economic risk as well as their traditional insurance risks. Considerable research in the international actuarial community is ongoing which attempts to model and manage these risks. Much of this research is building upon existing knowledge in financial mathematics. Equally, though, the specific problems being encountered are throwing back new challenges for financial mathematicians. This introduces us to the second theme: the issue of securitisation of insurance risks. This presents many new challenges that require a combination of actuarial mathematics, financial mathematics, mathematical economics and good contract design.

The workshop will bring together leading international experts from both academia and practice to promote exchange of ideas and help make progress on research into current issues.

Workshop Themes (further details below):

A: Stochastic asset models and asset-liability modelling for life insurance and pensions

B: Fair value, solvency testing and capital adequacy

C: Long-term risks: pricing and risk assessment

D: Dependence modelling, extreme-value theory, Levy processes and their application in insurance problems

E: Optimal stochastic control and optimal hedging problems in insurance

F: Issues relating to specific contracts and securitisation of insurance risks

Pre-registration and Registration Fees:

Interested persons should e-mail Andrew Cairns (A.Cairns@ma.hw.ac.uk). If you wish to present a paper please give Andrew an approximate title and an indication of which theme the paper falls under.

At the present time we don’t have an exact estimate of costs, but we may have some funds available to reduce fees for those speaking at the workshop.

Researchers already participating in the Developments in Quantitative Finance programme at the Isaac Newton Institute (see http://www.newton.cam.ac.uk/programmes/DQF/index.html ) may be able to apply to the Newton Institute for funding to attend the Edinburgh workshop.

Workshop structure:

Days 1 and 2 of the workshop will consist of talks (mostly invited) with a more applied or practical orientation and there will be the opportunity to register only for these two days. Days 3 to 5 will have a more academic flavour although with some further applied talks. The schedule on each day will allow for plenty of time for informal discussion between participants to encourage exchange of ideas.

Workshop themes (further details):

A: Stochastic asset models and asset-liability modelling for life insurance and pensions

Recent years have seen the need for the development of stochastic models which model a number of key variables affecting insurance companies: economic variables such as interest rates and price inflation; and other series directly relating to asset returns. Many financial institutions already use such models for internal asset-liability studies, to assess risks and also to manage their risks in some circumstances by altering investment strategies and their portfolio of liabilities. More recently regulators have begun to require the use of stochastic asset models for statutory reserving calculations.

B: Fair value, solvency testing and capital adequacy

Knowledge of the "fair value" of an insurance liability has increased in terms of importance in recent years as a result of changes first in international accounting regulations and second as actuaries see the benefit of the clarity revealed in using this as a method o liability valuation. Fair value can be interpreted as the price at which a liability would trade if a well informed and liquid market existed in this asset - even though such an asset is unlikely to exist at least in the near future. This allows shareholders to assess accurately the value of the company. Before the introduction of the use of "fair values", a variety of valuation techniques were used for liabilities that often had the effect of making it difficult for shareholders to establish the true value of an insurance company. In many cases liabilities incorporate substantial risks that are not diversifiable. As examples:

- natural catastrophes;

- systematic mortality risk (that is, unanticipated changes in population mortality rates);

- some pension liabilities are linked to salary growth which is a non-tradable economic risk.

As such there is a need for continued development of the principles as well as the practice underpinning fair value calculations. Financial mathematics and mathematical economics offer a range of alternative approaches to valuation in incomplete markets but there is little guidance as to which of these approaches is appropriate for insurance valuation.

Solvency testing and capital adequacy incorporates fair value but also goes beyond. Specifically stochastic reserving is becoming an important issue for insurers with practice and regulations beginning to mimic banking practice. Thus insurers need to be able to demonstrate that they have sufficient capital to withstand the risks they face (insurance, economic and financial risks) with a high probability. Here time horizons are generally much longer than those considered by banks and this presents insurers with some different issues.

C: Long-term risks: pricing and risk assessment

The issue of stochastic reserving for capital adequacy has been discussed already above. Long-term risks perhaps present greater problems for modellers. Short-term risks often can be hedged reasonably well using existing financial contracts in combination with suitably diversified portfolios of liabilities. For long-term risks pricing and hedging is more problematic. Some pensions and life insurance liabilities fall due many decades ahead and some of these incorporate financial guarantees. Portfolio risk management techniques which work well for banks for portfolios of short-term derivatives cannot be easily translated into methods for insurance companies: partly because no markets exist in relevant, long-dated assets, and partly because insurers cannot easily manipulate their portfolios of liabilities in the same way that a bank can its portfolio of derivatives.

Relevant subtopics:

- asset models designed for long-term economic "reasonableness";

- development of new financial markets which help insurers to manage their long-term insurance risks (e.g. mortality swaps);

- philosophical issues.

D: Dependence modelling, extreme-value theory, Levy processes and their application in insurance problems

Many of the issues raised above have specific aspects that may well be sensitive to the underlying stochastic processes and, for example, the dependencies between asset classes and certain liabilities. These sorts of issues are well known to have a substantial impact on short-term risks. It is less clear to what extent that these issues are important when we consider longer-term risk. It may be that model and parameter risk is much more important.

E: Optimal stochastic control and optimal hedging problems in insurance

There is a well-established body of research dealing with optimal investment and consumption in the financial economics literature, originally using the Hamilton-Jacobi-Bellman equation and more recently using the martingale approach. These methods have recently begun to find applications in insurance-related problems. Insurers and pension plans have become much more aware of the need to manage their risks effectively and this can be facilitated by using optimal control. To date research has focused on relatively simple models with a view to understanding which control variables do make a difference. There is considerable scope for future work of both a theoretical and an applied nature. For example, many problems in insurance involve incomplete markets, requiring a more-sophisticated theoretical base that many classical problems. On the applications side, many problems require numerical solution. However, the existing literature does not give much guidance on effective and accurate numerical methods.

F: Issues relating to specific contracts and securitisation of insurance risks

Many of the risks described above which are carried by insurers could be reduced by the use of practical hedging techniques and/or by the use of new traded securities which incorporate relevant insurance risks. This specific theme incorporates talks that might deal with the pricing and hedging of specific contracts. Examples might include catastrophe derivatives and guaranteed annuity options. Contract design here is a key factor. A poorly designed security may be too expensive or may not help insurers to an adequate extent, resulting in poor liquidity.