 |
The Third Workshop on
|
Analytical properties of some types of solutions to
nonlinear models in Financial Mathematics
L. A. Bordag
Abstract
We study uniqueness problems and
properties of families of solutions to option pricing models that
appeared last decade on the field of Financial Mathematics.
Different approaches - the Lie
point transformation method and the perturbation method
will illuminate the posed problem from different
points of view. Invariant solutions obtained for some of models with
help of a nontrivial Lie symmetry group and first results by using of
the perburbative method for the same models shows that the connection
between these two types of solutions is nontrivial, and uniqueness of
solutions can not be guaranteed for any set of admissible
parameters.