Comparison of solutions of stochastic equations and applications

Abstract

Pathwise comparison of solutions to a class of stochastic systems of differential equations is proved which extends the existing result of Geiβ and Manthey. When the diffusion coefficients are defferent, the Gal’čhuk-Davis method is extended to establish the comparision results. We illustrate our results with several examples some of which arise in stochastic finance theory

Keywords:

• DAAA04-94-G-0249
• Stochastic Differential Equations
• Comparision Theorems
• Applications to Finance