Abstract:

The research will concern the analysis and modelling of large systems of individual agents in the framework of incomplete or biased information. Both industrial and economic systems will be studied. The goal is to develop new methods and techniques allowing to quantify and control risk involved in random perturbations. For this purpose, it is necessary to provide a solid scientific foundation for the analysis, better understanding and proper design for various kinds of risk. We plan to extend the risk management methods studied in qualitative analysis of huge financial markets to general investment models.

The complexity and the size of data do not allow to study the above mentioned issues using traditional methodologies. Randomness of nature makes uncertainty ever present. There are various sources of uncertainty: a large number of objects (agents), their permanent (frequently instantaneous) fluctuations and random interactions, as well as the influence of external objective forces. Uncertainty often comes also from the external environment, which exhibits a random behaviour that is hard to predict and control. Consequently, decisions made under uncertainty are subject to risk.

Strategic objectives addressed

Strategic objective 1: Study of equilibria in complex systems.
Strategic objective 2: Optimization under uncertainty. .
Strategic objective 3: Study of large data systems..
Strategic objective 4: Information driven systems..
Strategic objective 5: Large markets..
Strategic objective 6: Decisions under uncertainty.

The programme of joint research activities is divided into 6 Sections:

1. Large systems
2. Modelling and control
3. Dependent fluctuations
4. Risk evaluation (
5. Uncertain volatility
6. Innovative products

which in turn are divided into 19 Workpackages

1. Large markets
2. Equilibria and arbitrage in large systems
3. Logical data analysis
4. Fairness and equity in systems design and operation
5. Stochastic control under uncertainty
6. Markets with transaction costs
7. Systems with defaults risk
8. Information flows in complex systems
9. Long range dependence
10. Non-Gaussian market models
11. Multidimensional analysis - copulas
12. Measures of risk
13. Ruin probability and operational risk
14. Heteroskedasticity in time series analysis
15. Stochastic volatility models and calibration
16. Term structure models
17. Evaluation of investments and real options
18. New commodity markets
19. Weather derivatives

Foreseen benefits of project

Development of existing and creation of new tools and methods for managing risk, which would allow to understand, predict and control (whenever possible and desirable) the business and investment risk. Risk is constantly present in all activities of the society. The long-term objective of the project is to develop a new innovative approach to complex management of risks. It is expected that since it will never be possible to completely eliminate the risk from all kinds of social activities, one of the benefits of the project would be to organise a durable network of European experts and their laboratories providing expertise in various aspects of risk management on a long term basis. As a consequence, the project will have a strong potential socio-economical impact through the improvement of competitiveness of European industry and the increase of efficiency of European resources. Results of the project should be readily applicable, though due to the necessity to work with huge amount of data and complexity of the models, certain stages of work will require additional prolonged efforts to be implemented. Therefore, the joint research activities of network's participants will be continued after the completion of the present project. A commitment for a moderate support for further activities of the network was already expressed by the Banach Center at the Institute of Mathematics of the Polish Academy of Sciences.

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