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The evaluation of systems dominated by uncertainty and complexity is now a very active and fertile field of research. These issues are also of great relevance to the social sciences, especially economics. However, for a variety of reasons progress in this latter discipline has not been as pronounced as in physics.

Economics has attempted to simplify analysis and developed mathematics appropriate to systems, which remain in continuous short and/or long time equilibrium. Thus homogeneous elements are frequently assumed —for example, the Capital Assets Pricing Model [CAPM] assumes all stock market investors have identical correct expectations about all investments. Models of 'General Equilibrium' remain a pinnacle of economic reasoning, although truly general models should be dynamic and not constrained to equilibrium conditions. 'Rational Expectations Economics' constructs models characterised by saddle path dynamics, but assumes that all economic agents know the precise location of the stable saddle path and jump to it instantly when disturbed from it by exogenous events. Many scientists from the community of business, economics and social science have been reluctant to come to grips with the unsettling difficulties of such research, although some economists such as Stiglitz and Markowitz have made progress. The availability of detailed and extensive data sets offers new opportunities. We believe that substantial progress is now possible by a direct transfusion of methods developed and well established by physicists.

Objective assessment of risk and quantitative representations of information that support decisions has a vital role to play in many other areas. Failure and fracture of engineering materials in structures and manufacturing processes are important areas for study. So-called real options and novel derivatives related to weather prediction are important to companies in the private sector. In the public sector the objective assessment of hazards plays a vital role in development of policy. A quantitative representation of hazard and risk would enable a major advance in ensuring food safety and in maintaining strong communications in areas of consumer concern. Quantitative methodologies are in place in some of areas and are being further developed as global standards, However it is frequently difficult to establish, with certainty, the size of potential hazards because direct, controlled experiments are simply not possible. Ethical dilemmas can prevent experiments on humans and repeating historical economic events is clearly impossible. Thus more often than not, unattributed safety factors are used to convert available evidence. Such an approach can lead to effective policies but these can be of a conservative nature. This can prevent the identification of dominant or particularly sensitive information sources, negate the use of specialist sources of information (e.g. impact on sub-populations) and obscure the role of uncertainties associated with other data sets. In making decisions, an assessment that provides a single quantitative framework and supports multiple calculations (including risks, costs and benefits), so that different end-users may consistently account for their distinct actions and choices, is needed.

Methods that are believed will contribute to major advances in the economic and social sciences include:

• New insights into the structure and dynamics of complex systems from non-linearity, 'emergence' and self-criticality. Perturbation of such systems, typified by systems such as sand-piles, earthquakes and microbial growth can lead to apparently unpredictable consequences. This behaviour seems common to and characterise many non-physical systems such as occur in biology, economics and systems of relevance to social scientists. Aspects of these issues have been discussed by, for example, Per Bak in 'How Nature Works'. Now physical scientists are playing a leading role in defining and developing these new territories, and showing the relevance of idealised models to the real world. These studies will provide new and important insights and offer new directions for physics research during the 21^st century research.
• Improved understanding surrounding the unbiased quantification and combination of non-numerical data sources (e.g. expert opinions) that can often dominate ill-defined problems. Concepts such as Bayesian Belief networks and fuzzy logic offer promise that may lead to new opportunities for both scientific understanding and innovation in a wide range of areas concerned with risk.
• Methods to analyse risk where the underlying probability distributions generate non-Gaussian distributions. Conventional risk estimation methods presume a Gaussian distribution, whereas it is now known that many processes generate non-Gaussian fat-tailed distributions. The failure of conventional economic, financial and actuarial models to take these real-world distributions into account when establishing their prices can have serious consequences. For example, it is arguable that the failure of Long Term Capital Management was due to its reliance upon models such as the Black-Sholes model of options pricing—which presumes a Gaussian distribution of disturbances in which multiple-standard-deviation disturbances are vanishingly rare—when the actual distribution of economically-relevant events is better approximated by power-laws or Levy distributions.
• Expanding computer power that brings very complex problems within the range of numerical representation. Its influence extends far beyond the predictions of the visionary John Von Neumann. Simulation, visualisation, artificial intelligence and inherently computational models such as cellular automata are creating a new paradigm for the way that science is advanced and exploited. Speed of computation has advanced to the point at which real-time analysis and control of large systems is feasible. Physicists and engineers have developed sophisticated technologies to simulate physical processes (including evolution). These technologies may now be applied to economic and social processes in ways that only a few economists and social scientists can currently envisage.

Physics and Risk

The physics and mathematics of risk may arguably be traced to the early work of Pascal, Bernoulli who flourished during what is commonly considered as the Age of the Enlightenment as Europe emerged from the Middle Ages and challenges to religious authority became widespread. The physicist Halley published the first actuarial tables before he studied astronomy. The British Government used these tables for many years afterwards. Malthus was the first to propose a quantitative model for the study of economic growth. This simple model has since been extensively developed and generalised by workers such as Lotka and Volterra and applied to numerous socio-economic and biological activities. It has been shown how the probability distribution for heavy tailed market returns emerges naturally from these models. The associated power laws are remarkably robust remaining constant even during quite dramatic changes of the model parameters. Using simple assumptions that have a bearing on social policy the values are in line with empirical observations. Further study is needed to identify mechanisms that may account for the complex time correlations that are known to exist in financial markets.

Physical models have proved a fertile source of inspiration in the study of socio-economic systems that are subject to shocks. These shocks can create a response in the economic system, which can have profound consequences, for example, asset price inflation and unemployment and which can be interpreted by reference to the shock excitation of a physical system. Models and information processing will be considered relevant to this problem.

Economic and financial databases relevant to shock and excitation modelling are in need of development. Vast amounts of data are now evolving and being stored. When understanding and modelling economic systems, an important issue is to develop the discernment to know how to filter the data and have access to relevant information.

A number of workers including some participants of this Action have begun exploring the characterisation of financial data using new approaches developed to deal with systems at the 'edge of chaos' where Bolzmann Gibbs Shannon approaches to information and entropy appear not to be appropriate. A decade ago, Tsallis proposed a new non-extensive measure for entropy. This has been applied widely to many physical systems. Recently, it has been applied to characterise financial data.

Data is vital to the development of understanding and insight of financial risk. It would be recommendable to establish a central database that will help gain further insight into stylized and common properties of financial time series especially the underlying correlation functions for prices, returns and volatility. This database should include not only contemporary data but also historical data. Analysis of such data can provide revealing insights into the evolution of the underlying social network.

Multi-Agents and Risk

It has long been recognized that financial market price fluctuations have their origin in demand generated by the interaction between agents (players or traders). Models of herding which explain the fat tails in the distribution of price changes, models of co-operation and adaptation (for example, 'prisoners dilemma' and minority games) and models of competitive auctions all have, at their heart, assumptions about a network of interacting agents.

More recently using principles of statistical physics researchers have made Monte Carlo simulations for Multi-Agent Models relevant to biology, medicine (including ageing), economics (percolation applied to stock markets), opinion formation and bank collapse. This new work is important in understanding, for example, routes to social consensus. For example, if people start with a random distribution of opinions about one question, how may a consensus be built? If such a consensus developed what is the distribution of times associated with opinion change of individuals? This is critically determined by the nature of the network and the nature of the links that form the network. In models, of the Ising type, that have been studied and applied by physicists to material systems during the 20^th century, the neighbors influence each network node. In a new development Sznajd has recently proposed a new concept where the node itself is the influencing agent. The persuasion flow in Sznajd models is thus opposite to that in Ising models and the results can be radically different.

The work outlined above together with other similar theoretical models is highlighting the important role of network structures in explaining many social phenomena such as market volatility, diffusion of innovation, technologies and convention and systemic risk. Further study is needed both to identify the principles that govern the formation, dynamics and growth of random networks and to understand how diffusive behavior is affected by the distribution of network links.

The important role of social and economic networks has been widely documented in empirical work. The output of this work is clearly of vital importance to policy makers who are increasingly faced with managing risk and taking decisions on fiscal and social measures relating, for example, to health, transport, epidemics such as aids and food crises and international conflict against changing population structures, attitudes, dynamics and demographics. It will also be of interest to business that needs to understand consumer choice in an increasingly complex market place.

Of especial interest are the opportunities to draw on models of mutation rates and mutational pressures that control the generation of asymmetric DNA where topology of the chromosome is important. Switching between DNA strands may be modeled in a similar manner to models of agent networks. An understanding of these issues could lead to new strategies of human reproduction and population diversity. Of particular interest to this action is how this work may help understand decision making under uncertainty and have important consequences for social policy and commercial strategy in say, insurance.

Prototype schemes for assessment of some microbial hazards using belief network representations have been developed. We shall develop schemes for the quantitative assessment of hazards using Bayesian belief representations. The Bayesian belief network is a kind of expert system that combines a graphical representation of a model domain with an efficient mathematical scheme for combining probabilities. Working in conjunction with food experts, schemes will be selected and designed to assist in the development of an integrated strategy for food safety assessment, management and communication. Implementation of the belief network structures involves quantification of the dependencies and available information. This involves construction of sets of conditional probabilities that express the chances of particular events given that other dependant events have already occurred, and the assignment of prior marginal probabilities that represent the current state of knowledge. Multiple integrals and convolutions may be used to aid the construction of conditional probability tables. Previous analyses have involved construction of tables of information sources presented as mechanical models, parameterized fits to data, statistical relationships and expert beliefs.

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