Skip to content
This repository has been archived by the owner on Jul 19, 2023. It is now read-only.

Test trivial HJBE for the simple driftless examples #48

Closed
jlperla opened this issue Feb 19, 2018 · 1 comment
Closed

Test trivial HJBE for the simple driftless examples #48

jlperla opened this issue Feb 19, 2018 · 1 comment

Comments

@jlperla
Copy link

jlperla commented Feb 19, 2018

After #46, we should go back through those examples and solve simple HJBE equations for the different cases of boundaries and variances. In general, pick a payoff function u ( x ) and a discount rate ρ > 0 , then for the operator A , the ODE to solve is
$$
\rho v(x) = u(x) + \mathcal{A} v(x)
$$
Or to setup the differential equation in a simpler form,
$$
(\rho I - \mathcal{A})v(x) = u(x)
$$
So we can solve the ODEs by lazily getting the B ( ρ I A ) operator and then solving B v ( x ) = u ( x ) . Discuss some examples of how to solve this with Chris.

@jlperla
Copy link
Author

jlperla commented Feb 21, 2018

Since we are only supporting the Dirichlet0 case for now, we don't need to worry about the affine issues. So test with v ( x ) = 0 and v ( x ) = 0 as well as v ( x ¯ ) = 0 reflecting

Sign up for free to subscribe to this conversation on GitHub. Already have an account? Sign in.
Labels
None yet
Projects
None yet
Development

No branches or pull requests

3 participants