Exchange rate bifurcation in a stochastic evolutionary finance model
type: Item
instance of: scholarly article
title: Exchange rate bifurcation in a stochastic evolutionary finance model
zbMATH Open document ID: 1264.91060
author: Gregory Gagnon
published in: Decisions in Economics and Finance
publication date: 2013-02-25T00:00:00Z
review text: The paper presents the monetary model of the exchange rate with a speculative bubble. A hybrid stochastic system for the financial market involving a discrete time process and a continuous time process is constructed. The discrete time process models the bubble and the continuous time process is a stochastic differential equation for monetary policy together with a backward stochastic equation for the exchange rate. Stability and bifurcation theorems for such dynamical system from evolutionaty finance are proved. The bubble process is nonlinear and interacts with the money supply process. The stability results do not follow from existing results on stochastic differential equations. Moreover, the stability theorems have important input into a fluctuation theorem. Some directions for the future research are proposed.
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 35Q91
Mathematics Subject Classification ID: 91G70
zbMATH DE Number: 6138702
zbMATH Keywords: evolutionary finance
zbMATH Keywords: speculative bubble
zbMATH Keywords: stochastic differential equation
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s10203-011-0113-3
OpenAlex ID: W2076316179
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DOI: 10.1007/S10203-011-0113-3
description: scientific article; zbMATH DE number 6138702