Term structure extrapolation and asymptotic forward rates

We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the European insurance supervisor EIOPA. We use the characterization of the Smith–Wilson class of interpolating functions as the solution to a functional optimization problem to extend their approach in such a way that forward rates will converge to a value which is an outcome of the optimization process. Precise conditions are stated which guarantee that the optimization problems involved are well-posed on appropriately chosen function spaces. As a result, a well-defined optimal asymptotic forward rate can be derived directly from prices and cashflows of traded instruments. This allows practitioners to use raw market data to extract information about long term forward rates, as we will show in a study which analyzes historical EURIBOR swap data.     

Lyapunov exponents and asymptotic dynamics in random Kolmogorov models

The current paper is devoted to the investigation of asymptotic dynamics in random Kolmogorov models. Applying the theory of principal Lyapunov exponents and the principal spectrum developed in the authors previous papers together with the concept of part metric it provides conditions for the existence of a globally attracting positive random equilibrium, the existence of a globally attracting uniformly positive random equilibrium, and the extinction in random Kolmogorov models. These results are an important complement to the existing ones.     

The local asymptotic minimax adaptive property of a recursive estimate

A locally asymptotically normal estiamtion problem generated by independent and identically distributed generalized random variables is considered. A recursive estimate based on a stochastic approximation method, a modification of an estimate proposed by Sakrison, is shown to be locally asymptotically minimax. For a nonparametric generalization of the estimation problem, a modification of the estimate is shown locally asymptotically minimax adaptive.     

Topological structure of Urysohn universal spaces

The main aim of the paper is to prove that every nonempty member P of the algebra of subsets of a nontrivial Urysohn space generated by all balls (open and closed) is an l₂-manifold of finite homotopy type. An algorithm of finding a polyhedron K such that P and K×l₂ are homeomorphic is presented. An alternative proof of the Uspenskij theorem [V.V. Uspenskij, The Urysohn universal metric space is homeomorphic to a Hilbert space, Topology Appl. 139 (2004) 145-149] is given.     

A multi-structural framework for adaptive supply chain planning and operations control with structure dynamics considerations

A trend in up-to-date developments in supply chain management (SCM) is to make supply chains more agile, flexible, and responsive. In supply chains, different structures (functional, organizational, informational, financial, etc.) are (re)formed. These structures interrelate with each other and change in dynamics. The paper introduces a new conceptual framework for multi-structural planning and operations of adaptive supply chains with structure dynamics considerations. We elaborate a vision of adaptive supply chain management (A-SCM), a new dynamic model and tools for the planning and control of adaptive supply chains. SCM is addressed from perspectives of execution dynamics under uncertainty. Supply chains are modelled in terms of dynamic multi-structural macro-states, based on simultaneous consideration of the management as a function of both states and structures. The research approach is theoretically based on the combined application of control theory, operations research, and agent-based modelling. The findings suggest constructive ways to implement multi-structural supply chain management and to transit from a “one-way” partial optimization to the feedback-based, closed-loop adaptive supply chain optimization and execution management for value chain adaptability, stability and crisis-resistance. The proposed methodology enhances managerial insight into advanced supply chain management.     

Conservation laws and asymptotic behavior of a model of social dynamics

A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions is investigated both analytically and computationally. Existence, stability and attractivity of certain equilibria are proved.     

Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity

Mathematical Programming - In a Hilbert space setting $${{mathcal {H}}}$$ , we study the fast convergence properties as $$t rightarrow + infty $$ of the trajectories of the second-order...     

Metriplectic structure, Leibniz dynamics and dissipative systems

A metriplectic (or Leibniz) structure on a smooth manifold is a pair of skew-symmetric Poisson tensor P and symmetric metric tensor G. The dynamical system defined by the metriplectic structure can be expressed in terms of Leibniz bracket. This structure is used to model the geometry of the dissipative systems. The dynamics of purely dissipative systems are defined by the geometry induced on a phase space via a metric tensor. The notion of Leibniz brackets is extendable to infinite-dimensional spaces. We study metriplectic structure compatible with the Euler-Poincaré framework of the Burgers and Whitham-Burgers equations. This means metriplectic structure can be constructed via Euler-Poincaré formalism. We also study the Euler-Poincaré frame work of the Holm-Staley equation, and this exhibits different type of metriplectic structure. Finally we study the 2D Navier-Stokes using metriplectic techniques.     

On asymptotic efficiency and deficiency of some adaptive tests in the one-sample problem

In this paper, we consider adaptive tests for the one-sample problem and investigate the order of difference between the power of a given adaptive asymptotically efficient test and that of the most powerful test. Here adaptation means that the efficient score function of the test is estimated from the sample. A Fourier series estimator is used for the score function. Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446). Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

Transient and asymptotic dynamics of a prey–predator system with diffusion

In this paper, we study a prey–predator system associated with the classical Lotka–Volterra nonlinearity. We show that the dynamics of the system are controlled by the ODE part. First, we show that the solution becomes spatially homogeneous and is subject to the ODE part as t → ∞ . Next, we take the shadow system to approximate the original system as D → ∞ . The asymptotics of the shadow system are also controlled by those of the ODE. The transient dynamics of the original system approaches to the dynamics of its ODE part with the initial mean as D → ∞ . Although the asymptotic dynamics of the original system are also controlled by the ODE, the time periods of these ODE solutions may be different. Concerning this property, we have that any δ > 0 admits D₀ > 0 such that if , the time period of the ODE, satisfies , then the solution to the original system with D ≥ D₀ cannot approach the stationary state. Copyright © 2012 John Wiley & Sons, Ltd.     

Uniform global asymptotic stability of adaptive cascaded nonlinear systems with unknown high-frequency gains

We study adaptive tracking problems for nonlinear systems with unknown control gains. We construct controllers that yield uniform global asymptotic stability for the error dynamics, and hence tracking and parameter estimation for the original systems. Our result is based on a new explicit, global, strict Lyapunov function construction. We illustrate our work using a brushless DC motor turning a mechanical load. We quantify the effects of time-varying uncertainties on the motor electric parameters.