You are right, the absolute value-like term creates a singularity in Dphi, but not in phi itself. One often gets equations of this form in control problems, especially if the Hamiltonian is linear in some of the controls, or if the controls are bounded. Solutions to these types of equations can have discontinuities in the derivatives, which form boundaries between different solution regions, so those boundaries need to be treated with care. I'm hoping FiPy can handle that.
What do you mean by looking at the dual problem? _____________________________________________ Douglas L. Borden Knight Equity Markets, L.P. 545 Washington Boulevard, Jersey City, NJ 07310 Tel: 201-239-2208 | Email: [email protected] Fax: 201-356-2279 | AIM: DBordenAtKnight Cell: 646-416-4875 | Skype: DBordenAtKnight LinkedIn: www.linkedin.com/in/douglasborden _____________________________________________ ________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of Frederic Boyer Sent: Tuesday, October 13, 2009 3:19 PM To: Multiple recipients of list Subject: Re: Need help getting started The absolute value will create a singularity... what are the stochastic equations that lead to that PDE? Looks to me like looking at the dual problem would make more sense numerically. On Tue, Oct 13, 2009 at 11:01 AM, Borden, Doug <[email protected]<mailto:[email protected]>> wrote: Hello, I've just started using FiPy for a problem in quantitative finance, and I need a bit of help getting started. I've cast a particular problem in trading as a stochastic control problem, and after deriving the relevant Hamilton-Jacobi-Bellman equation, I end up with a PDE to solve (see attached PDF). I have two questions: 1) Do I only have a source term and a transient term, or can I cast my problem with a convection term? 2) How do I specify my boundary conditions? Any help you can offer would be greatly appreciated. Best Regards, Doug Borden -------------------------------------------- Douglas L. Borden, Managing Director T: 201.239.2208 | F: 201.356.2279 | C: 646.416.4875 Email: [email protected]<mailto:[email protected]> | AIM: DBordenAtKnight LinkedIn: www.linkedin.com/in/douglasborden<http://www.linkedin.com/in/douglasborden> [cid:[email protected]] Knight Equity Markets, L.P. 545 Washington Boulevard | Jersey City, NJ 07310 -------------------------------------------- DISCLAIMER: This e-mail, and any attachments thereto, is intended only for use by the addressee(s)named herein and may contain legally privileged and/or confidential information. If you are not the intended recipient of this e-mail, you are hereby notified that any dissemination, distribution or copying of this e-mail and any attachments thereto, is strictly prohibited. If you have received this in error, please immediately notify me and permanently delete the original and any printout thereof. E-mail transmission cannot be guaranteed to be secure or error-free. The sender therefore does not accept liability for any errors or omissions in the contents of this message which arise as a result of e-mail transmission. NOTICE REGARDING PRIVACY AND CONFIDENTIALITY Knight Capital Group may, at its discretion, monitor and review the content of all e-mail communications. http://www.knight.com<http://www.knight.com/>
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