Central Economics and Mathematics Institute

About: Central Economics and Mathematics Institute is a facility organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Foreign-exchange reserves. The organization has 297 authors who have published 580 publications receiving 6449 citations. The organization is also known as: Federal State Institution of Science Central Economics and Mathematics Institute of the Russian Academy of Sciences.

Bond Market Structure in the Presence of Marked Point Processes

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.

Towards a general theory of bond markets

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.

Optional decomposition and Lagrange multipliers

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.

Negative-cycle detection algorithms

Abstract: We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We survey cycle detection strategies, study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of out discoveries is that a cycle detection strategy of Tarjan greatly improves computational performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of out study, we develop problem families for testing negative cycle algorithms.