** Vorobyov O.Yu., Novosyolov A.A., Simonov K.V., Fomin A.Yu.**
Portfolio Analysis of Financial Market Risks by Random Set Tools.
Proceedings of the Symposium "Risks in Investment
Accumulation Products of Financial Institutions",
Schaumburg, IL, 2001, p. 43-66.
** Abstract**.
A new approach to portfolio analysis of financial market risks
by random set tools is considered. Despite many attempts, the
consistent and global modeling of financial markets remains
an open problem. In particular it remains a challenge to find
a simple and tractable economic and probabilistic approach to
market modeling. This paper attempts to highlight fundamental
properties that a market model should possess. The paper suggests
a random set approach as a probabilistic base of this model. Using
this approach it is possible to establish a corresponding
interactive market dynamics that involves a minimal number of sets.
These sets include the set of capital surpluses, the set of capital
within assets and the set of capital deficits. Several interesting
properties related to random volatility of assets quality, probabilities
of quality categories and defaults and matrices of transition
probabilities of switching among categories can be derived.
In addition the random set approach allows to derive the so
called transition set-matrices, random set invariants of capital
redistribution processes. Empirical evidence will be given that
confirm these random set findings. The approach is also illustrated
by collapses in U.S. financial markets in 90's and can be used to
explain Russian default'98.