Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 19181, 24 pages
doi:10.1155/JAMDS/2006/19181
Abstract
This paper finds fundamental solutions to the backward Kolmogorov
equations, usually interpretable as transition density functions
for variables x that follow certain stochastic processes of the
form dx=A(x,t)dt+cxydX and dx=A(x,t)dt+α1+α2x+α3x2dX. This is achieved by first reducing the relevant PDEs
that the density functions satisfy to their canonical form. These
stochastic processes have direct realistic applications in the
modeling of financial assets.