[Quantlib-users] Ideas on finite difference engine

[Joseph W. <jo...@co...>]

Here are some very rough ideas on modifying the finite difference engine 
to handle systems of PDE's.  Please feel free to point out flaws and 
problems in these ideas, as I'd like to have a consensus that this 
redesign is in the right direction before I start any coding.

The first issue is how to represent a system of PDE's.  I propose two 
objects

StateModel - Which is an abstract object that represents the current 
state of the system

and

DynamicalModel - which is an object that includes one or more operators 
and boundary conditions, step condition for the operators.

The idea that I'm playing with is to create an TimeStepper object which 
sits under the FiniteDifferenceModel, takes the StateModel and 
DynamicalModel and time steps it one step.  The TimeStepper object would 
then use the infrastructure of operators and such to calculate a single 
time step.

It also occurs to me that the first thing that could be done with this 
infrastructure is to clean up the ControlVariate code.  The system of 
PDE's would include both the price and the control prices in a single 
framework.  To retrofit the current code, we'd create a

SingleFunctionStateModel (i.e. a grid) and
SingleFunctionDynamicalModel (which encapuslates the operator, the 
boundary conditions, and the step function conditions in one object)

As far as use cases, right now I'm thinking about two

* allowing the calculation of convertible bonds through the TF model
* making the control variate code a bit more elegant.  One could put 
both the main equation and the control variate equation into the same 
system.  Also, one could create an addControlVariate function which 
would take a dynamic system and create a new dynamic system with a 
control variate added.

Thoughts....

Thoughts?