he origin
of mean reverting equation as stated below was discussed in the section
(
Solving
one dimensional mean reverting equation
).
According to the summary (
Free
boundary problem 2
), the function
also solves the following free boundary problem.
Let
and
We multiply the above PDE with a smooth function
,
,
integrate over
and do integration by parts. We
get
We add the penalty term according to the recipe
(
Variational
inequalities in maximization case
). We arrive to the following penalized
problem.
