Showing papers by "Central Economics and Mathematics Institute published in 1998"

Asymptotic arbitrage in large financial markets

Abstract: A large financial market is described by a sequence of standard general models of continuous trading. It turns out that the absence of asymptotic arbitrage of the first kind is equivalent to the contiguity of sequence of objective probabilities with respect to the sequence of upper envelopes of equivalent martingale measures, while absence of asymptotic arbitrage of the second kind is equivalent to the contiguity of the sequence of lower envelopes of equivalent martingale measures with respect to the sequence of objective probabilities. We express criteria of contiguity in terms of the Hellinger processes. As examples, we study a large market with asset prices given by linear stochastic equations which may have random volatilities, the Ross Arbitrage Pricing Model, and a discrete-time model with two assets and infinite horizon. The suggested theory can be considered as a natural extension of Arbirage Pricing Theory covering the continuous as well as the discrete time case.

Rapid Growth Paths in Multivalued Dynamical Systems Generated by Homogeneous Convex Stochastic Operators

Abstract: The paper examines dynamical systems generated by convex homogeneous multivalued operators in spaces of random vectors. The primary goal is to investigate the growth rates of random trajectories of these dynamical systems. Existence and characterization theorems for ‘rapid’ trajectories, growing faster in a certain sense than others, are obtained.

The structure of optimal synthesis in a neighbourhood of singular manifolds for problems that are affine in control

Abstract: The question of the classification of the phase portraits of optimal synthesis in a neighbourhood of a singular universal manifold is discussed for systems of constant rank that are affine in control. Both phase state and control are assumed to be many-dimensional. The classification is based on the order of the singular extremals and the property of involutiveness (or otherwise) of the velocity indicator. The synthesis of optimal trajectories is shown to be a space fibred over the base W consisting of singular optimal trajectories; its fibres are non-singular optimal trajectories. If the control is many-dimensional, then W is a stratified manifold. In the involutive case the fibres are one-dimensional. In the non-involutive case the fibres are many-dimensional and contain chattering trajectories; the dimension of the fibres and the structure of the field of trajectories in the fibres depend on the order of the singular extremals.

Transition to a Market-Oriented Economy: China versus Eastern Europe and Russia

Abstract: For the transition from a centrally planned economy to a decentralized market economy, there are two different approaches. The first is a ‘big bang’ or ‘shock therapy’ approach; the reforms undertaken in Eastern Europe and the former USSR in recent years are typical examples. This approach considers stabilization, marketization, and privatization to be the necessary components of a successful transition and attempts to complete all these components simultaneously or in a short sequence. The contrasting alternative is the ‘gradual’, ‘organic’, or ‘evolutional’ approach, and this latter has characterized China’s recent reforms. It is piecemeal, partial, incremental, sequential, often experimental, and without large-scale privatization.

An alternative model of spatial competition

Abstract: In this paper, an alternative network model of oligopolistic markets of homogeneous product is developed. The agents sell their product at several independent markets taking into account the prices of the product unit at different markets, production expenditures, and transportation costs. The unit price at a market depends upon the total supply, whereas the production expenditures may grow along with the total volume of output by all producers. The latter ones choose production volumes and distribution of the output fractions sold at the markets. In order to do that, each agent uses conjectures about the total market supply variations depending upon those of his own supply. Under general enough assumptions concerning the market inverse demand functions and the producers’ cost and transportation functions, the equilibrium existence and uniqueness theorems are formulated and proven. Thus, the paper could be considered as a contribution to the analysis of the structuring effect of transportation network on markets and society as a whole.

On Hilbert series and the homology of PI-algebras

Abstract: The main goal of this paper is to generalize the criterion for complete intersections well known in commutative algebra to the case of an arbitrary variety of PI-(super)algebras. As a consequence, formulae are obtained for computing the Hilbert series of the even and odd parts of relatively free superalgebras and free special Jordan superalgebras.

Optional Decomposition and Lagrange Multipliers

Abstract: Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand phi such that the difference X-phi times S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.

Internal Rate of Return Index and its Modifications (in Russian)

Abstract: We investigate various properties of the internal rate of return (IRR) metric for investment projects. It is known that this metric does not exist or is not uniquely defined for many projects. Therefore many suggestions for replacing it by some modified indexes with a wider domain of definition are known to exist. Such sugestions are considered in the paper with a general inference as to their inappropriateness. On a positive side, we offer a system of axioms reflecting the basic properties of IRR and present the structure of “return indexes” which would satisfy such axioms. It is demonstrated that as long as the projects with identical “return indexes” maintain affine transformation along the time axis, such indices would coincide (accurate to a monotonous smooth transformation) with the “usual” IRR. An issue of defining “profitability indices” for projects with random cash flows is considered as well. Note: The downloadable document is in Russian.

Ergonomic Provisions of the Shelter's Safety at the Chernobyl Nuclear Power Plant

Abstract: This paper outlines the main Human Factors/Ergonomic tasks to be solved to enhance the safety of the Shelter (Sarcophagus) of the Chernobyl Nuclear Power Plants's destroyed Unit #4 during current maintanance and forthcoming reconstruction as were observed during our visit to this site. The convential Human Factors problems are connected to personnel activities such as: traffic organization, radiation cartography, communications, monitoring of the personnel activity inside the Shelter, protective clothes, instruments, illumination, and ventilation. Macroergonomic problems include: uncertainty, risk to health, and high technical level of instruments and equipment used. Shelter workers have to assimilate many different professions and the scope of their training needs to be very large. Both situational and spatial uncertainties of the Shelter set special training problems. Three dimensional models and virtual reality tools are needed to help in solve these problems. Psychological training should also be conducted. The investigation was performed within the framework of cooperation between Russian an American ergonomists (Parsons et al. 1992).