Exchange rate bifurcation in a stochastic evolutionary finance model
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.
scientific article; zbMATH DE number 6138702