Abstract:
The Bermudan option pricing problem with variable transaction costs is considered
for a risky asset whose price process is derived under the information-based
model.
The
price
is
formulated
as
the
value
function
of
an
optimal
stopping
problem,
which
is
the
val
ue
function
of
a
stochastic
control
problem
given
by
a non-linear
second
order
partial
differential
equation.
The
theory
of
viscosity
solutions
is
applied
to
solve
the
stochastic
control
problem
such
that
the
value
function
is
also
the
solution
of
the
corresponding
Bellman
equation.
Under
some
regularity
assumptions,
the
existence
and
uniqueness
of
the
solution
of
the
pricing
equation
are
derived
by
the
application
of
the
Perron
method
and
Banach
Fixed
Point
theorem.
