arXiv subjects

Viktors Ajevskis

Publications and source records attributed to Viktors Ajevskis.

3 recordsLinked to original sources

arXiv2015

An Exchange Rate Target Zone Model with a Terminal Condition and Mean-Reverting Fundamentals

This paper proposes a target zones exchange rate model with a terminal condition of entering a currency zone. It is assumed that the exchange rate is a function of the fundamental and time. Another essential assumptions of the model is that the fundamental process is bounded inside a band and that terminal condition for the exchange rate holds. The fundamental is specified in two ways: as a regulated Brownian motion and Ornstein-Uhlenbeck processes. For the case of the Brownian motion process the closed form solution of the problem is obtained, whereas for the Ornstein-Uhlenbeck process the closed form solution does not exist, therefore we had to use numerical method for solving of the problem. Both specifications are compared numerically.

econ.GN↗

arXiv2015

Nonlocal Solutions to Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and the fact that solutions to general equilibrium models converge to a steady state. The approach allows deriving the a priori and a posteriori approximation errors of the solutions. Under certain nonlocal conditions we prove the convergence of the approximate solutions to the true solution and hence the Stable Manifold Theorem. We also show that the proposed approach can be treated as a rigorous proof of convergence for the extended path algorithm to the true solution in a class of nonlinear rational expectation models.

econ.GN↗

arXiv2015

Semi-Global Solutions to DSGE Models: Perturbation around a Deterministic Path

This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i.e. the model where the volatility of the shocks vanishes. If a deterministic path is global in state variables, then so are the constructed solutions to the stochastic model, whereas these solutions are local in the scaling parameter. Under the assumption that a deterministic path is already known the higher order terms in the expansion are obtained recursively by solving linear rational expectations models with time-varying parameters. The present work also proposes a method rested on backward recursion for solving general systems of linear rational expectations models with time-varying parameters and determines the conditions under which the solutions of the method exist.

econ.GN↗