Decision-making when facing random in a broad sense phenomena

Exploitable results

The problem dealt with in this one year contract was quite circumscribed, but nevertheless quite far-reaching: many statistics are the result of many "small and unknown" causes, but don not produce entirely stable distributions. They are not "random" in the strict sense of the word, yet, they are in a broader sense. How to use these statistics to feed and/or illustrate economic models? This question was related to the theory of dynamic systems, more accurately to the theory of multivalued semidynamic systems, a new mathematical tool to model economic systems. The above question was regarded as an application of such a theory. 1.The foundation of the theory of multivalued semidynamic systems was developed. Multivalued semiflows were introduced and their global attractors were studied. These abstract results were used of the study of the limit behaviour of non-linear dynamic systems, the initial state of which do not define uniquely future behaviour. This broad group of systems includes systems under certainty, systems with nonunique solutions, and systems that are described by differential inclusions, etc. The new approach to study operator and differential inclusions was developed. 2.One application was performed on Georgian data. The global price levels depends on global money supply and, to some extent alos, on the level of real global output. There is, in addition, a certain time lag between growth of money supply and the triggering of inflationary forces, which accelerate the rate of price level increase. As there is also an impact of the inflation rate on real money supply, hence on the interest rate, conditions for the emergence of multivalued semi-dynamic system are met. The methods developed were then used to estimate, in particular, the time lag between growth of money and the acceleration of price level increases. This helps of course to better forecasts of the inflation rate. 3.Other applications are currently sought to decision making under risk and uncertainty and further developments of the statistical regularities entailed by such systems are to be expected.

Exploitable results

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