Kolmogorov Backward Equation

DogonMatrix · July 25th, 2003, 12:26 pm

Is there a standard way to solve the KBE ? And in general is there a classic reference on solving differential equation for financial derivatives?Thanks

elan · July 25th, 2003, 12:35 pm

QuoteOriginally posted by: DogonMatrixIs there a standard way to solve the KBE ? And in general is there a classic reference on solving differential equation for financial derivatives?ThanksNo standard / classic references yet. A lot of good stuff on solution techniques can be found in the physics books:1. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry2. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences 3. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications

Mukuzani · July 25th, 2003, 3:04 pm

The immortal classic isH.S. Carslaw & J.C. Jaeger, Codduction of Heat in Solids.for American options see also J. Crank, Free and Moving Boundary Problems.In Finance PW is the best.

DogonMatrix · July 25th, 2003, 3:49 pm

Thanks. Mukuzani, I suppose by PW you mean our host Paul Wilmott, but are you refering to ' Derivatives' or 'Mathematics for financial derivatives' ?

Mukuzani · July 25th, 2003, 4:52 pm

I mean "Derivatives" that is always on my desk. PWQF is the extension of this book. If you want to learn about the methods of PDE solutions the differences are not important. Sorry, I don't remember what is in 'Mathematics for financial derivatives' For more systematic approach follow elan's recommendation or take any book on Equations of Mathematical Physics and read chapters on Parabolic Equations.My favorite is Samarskii and Tikhonov http://www.amazon.com/exec/obidos/tg/de ... s&n=507846