the mean reverting equation in preparation to an experiment in stochastic
optimization. The mean reverting equation was introduced in the section
Mean reverting equation
make all parameters constant. A quantity
is given by an
where the quantity
is a value of some observable market parameter that enters into a piecewise
linear payoff function. We calculate an equation for
of such shape is called "butterfly" payoff. One reason for choosing such
payoff becomes apparent right away.
According to the section (
), the function
is also a solution of the following problem.
(Strong mean reverting problem) Find
We transform to a problem with homogeneous boundary conditions. Let
(Strong mean reverting problem 2)