IJPAM: Volume 49, No. 1 (2008)

A COUPLED STOCHASTIC DIFFERENTIAL MODEL IN
FINANCE UNDER LOCAL LIPSCHITZ NONLINEARITY

T.E. Govindan$^1$, Carlos Ibarra-Valdez$^2$, J. Ruiz de Chávez$^3$
$^1$Department of Mathematics, ESFM
Instituto Politécnico Nacional
México D.F., 07738, MEXICO
e-mail: tegovindan@yahoo.com
$^{2,3}$Departamento de Matematicas
Universidad Autonoma Metropolitana - UAM
Unidad Iztapalapa
Av. San Rafael Atlixco No. 186, Col Vicentina
A.P. 55-534, Iztapalapa, Mexico D.F., 09340, MEXICO
$^2$e-mail: ibvc@xanum.uam.mx
$^3$e-mail: jrch@xanum.uam.mx


Abstract.A local Lipschitz condition for a dynamical stochastic coupled model of financial markets is considered. Existence and uniqueness of solutions and their continuous dependence with respect to the initial conditions are established. This generalization of the usual Lipschitz assumption allows to include as examples, markets with time-varying interest rates and volatilities, among others.

Received: October 25, 2008

AMS Subject Classification: 60H10, 62P05

Key Words and Phrases: stochastic coupled model, trading, Itô equation, local Lipschitz condition, existence and uniqueness of a solution, continuous dependence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1