Showing papers by "Central Economics and Mathematics Institute published in 1997"
TL;DR: In this paper, the authors investigated the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process and proved the existence of a time-independent set of basic bonds.
Abstract: We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory that allows for measure–valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener–Poisson model we prove the existence of a time–independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure.
366 citations
TL;DR: It is shown that a market is approximately complete iff an equivalent martingale measure is unique and two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions are suggested.
Abstract: To the memory of our friend and colleague Oliviero Lessi. Abstract. The main purpose of the paper is to provide a mathematical back- ground for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trad- ing strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.
253 citations
TL;DR: This paper gives a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.
Abstract: Let \({\cal Q}\) 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 \({\cal Q}\). The optional decomposition theorem for \(X\) states that there exists a predictable integrand \(\varphi\) such that the difference \(X-\varphi\cdot S\) 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.
177 citations
TL;DR: By using the topological degree the concept of ’’exceptionalfamily of elements‘‘ specifically for continuous functions is introduced, which has important consequences pertaining to the solvability of the explicit, the implicit and the general order complementarity problems.
Abstract: By using the topological degree we introduce the concept of ’’exceptional family of elements‘‘ specifically for continuous functions. This has important consequences pertaining to the solvability of the explicit, the implicit and the general order complementarity problems. In this way a new direction for research in the complementarity theory is now opened.
96 citations
TL;DR: In this paper, the limiting hedging error of the Leland strategy for the approximate pricing of the European call option in a market with transactions costs was shown to be not equal to zero in the case when the level of transactions costs is a constant, in contradiction with the claim in Leland.
Abstract: We compute the limiting hedging error of the Leland strategy for the approximate pricing of the European call option in a market with transactions costs. It is not equal to zero in the case when the level of transactions costs is a constant, in contradiction with the claim in Leland (1985).
95 citations
TL;DR: In this paper, it was shown that the Pareto property is inconsistent with nondictatorship for social choice rules defined on two-dimensional choice spaces, and they considered applications of this result in higher dimensions.
Abstract: We establish that the Pareto property is inconsistent with nondictatorship for social choice rules defined on two-dimensional choice spaces. In addition, we consider applications of this result in higher dimensions.
14 citations
TL;DR: In this article, divergence theorems are proved in a mass formulation for non-topological variants of the mass transfer problem and of related extremal marginal problems, and a connection between two types of problem is investigated (problems with fixed difference between the marginal measures, and problems with fixed marginal measures).
Abstract: Duality theorems are proved in a mass formulation for non-topological variants of the mass transfer problem and of related extremal marginal problems. The connection between two types of problem is investigated (problems with fixed difference between the marginal measures, and problems with fixed marginal measures), and a criterion for their equivalence is obtained.
12 citations
TL;DR: In this article, the authors present a method of treatment extremal problems with degenerate equality constraints, originally proposed by A.A. Milyutin, which consists of the passing from the given problem to another one, in which the equality constraints are nondegenerate.
Abstract: It is well known in the theory of extremal problems that the abnormal case, i.e. the case when equality constraints are degenerate at the examined point, is a difficult subject to obtain higher order conditions of a local minimum. Especially it is true for necessary conditions. The matter is that “standard” necessary conditions, relevant to the general case, are always trivially fulfilled in the abnormal case and do not provide any information about the presence or absence of a local minimum at the given point. Here we present a method of treatment extremal problems with degenerate equality constraints, originally proposed By A.A. Milyutin. It consists of the passing from the given problem to another one, in which the equality constraints are nondegenerate. Application of this method and of its refinement allows one to obtain informative quadratic order necessary conditions for local minima in some classes of problems.
12 citations
01 Jan 1997
TL;DR: Duality theory for nontopological versions of mass transfer problem extending the classical Monge-Kantorovich problem is developed in this paper, where applications to dynamic optimization and approximation theory are outlined.
Abstract: Duality theory for nontopological versions of mass transfer problem extending the classical Monge-Kantorovich problem is developed. Applications to dynamic optimization and approximation theory are outlined.
8 citations
TL;DR: In this article, the authors examine the trend towards commercialization of Russian Space rockets via joint ventures with Western firms and analyze the reasons for both sides' involvement (financial, competitive) and discuss the background, status and prospects of a number of specific joint ventures.
7 citations
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TL;DR: In this paper, the limiting hedging error of the Leland strategy for the approximate pricing of the European call option in a market with transactions costs was shown to be not equal to zero in the case when the level of transactions costs is a constant, in contradiction to the claim in Leland.
Abstract: We compute the limiting hedging error of the Leland strategy for the approximate pricing of the European call option in a market with transactions costs. It is not equal to zero in the case when the level of transactions costs is a constant, in contradiction to the claim in Leland (1985).
TL;DR: The productivity factor is included in the individual state space and the main dynamic equation is derived which takes into account the stochastic fluctuations of scientific community members' productivity and some modifications of the Fokker-Planck equation.
Abstract: The productivity factor is very important at the mathematical simulation of scientific community evolution. In Ref. 1 the productivity index has been incorporated into the model exogenously to formulate the criterion of dynamic optimization of the scientific community age structure. In this paper we are going to include the productivity (as well as the age) in the individual state space and to derive the main dynamic equation which takes into account the stochastic fluctuations of scientific community members' productivity and some modifications of the Fokker-Planck equation. An approximation method for the evolution model is suggested with the aid of which the computational experiment is carried out. The discussion of experimental results and possible ways for improvement and extension of model are presented.
TL;DR: In this article, it was shown that the distribution of demand vectors derived from a not necessarily metonymic population is identical with the distribution derived from some metonymically population, which implies that the metonymy hypothesis cannot be rejected or confirmed on the basis of data from a single cross-section.
TL;DR: In this article, a new approach is proposed for research on existing and potential international conflicts at the global and local levels, based on economic, social, demographic, environmental, and political factors of instability.
Abstract: This chapter is devoted to the urgent problem of forecasting conflicts on the basis of economics and mathematical models. A new approach is proposed for research on existing and potential international conflicts at the global and local levels, based on economic, social, demographic, environmental, and political factors of instability. At the global level, the analysis is based on major features of the main civilizations and on indicators of environmental tension, particularly in the relations between West European (Mediterranean) and Islamic (Arab) civilizations; Islamic (Turkic) and Eastern Christian civilizations; and Eastern Christian countries and the People’s Republic of China. A method is described for predicting conflicts on the basis of estimation, modeling, and comparison of military capital. At the local level, characteristics are given of the local conflicts in the Commonwealth of Independent States (CIS) and the model of dynamics and procedure for settling armed conflicts with the help of a regional leader. The results, which are based on economic data, permit a deeper understanding of geopolitical and environmental processes. On this basis we develop recommendations aimed at preventing conflicts.