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April 8th, 2012, 12:21 PM  #1 
Newbie Joined: Apr 2012 Posts: 1 Thanks: 0  Finding the general solution to the Black Scholes PDE
Hello, I have the PDE ?v/?? + 1/2(?^2)(?^2)?^2v/??^2 + (1/T +(Dr)?)?v/??=0 and firstly I need to seek a solution of the form v=?1(?)? + ?0(?) and then determine the general solution for ?1(?) and ?0(?). I am given that ?=I/TS  X/S and ?=Tt. Could anybody help me with this? Thanks 
August 23rd, 2012, 03:47 AM  #2 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3  Re: Finding the general solution to the Black Scholes PDE
Hey manchester29. There is a book by Wilmott, Howison, and DeWynne called "The Mathematicas of Financial Derivatives" that goes over the proof to transform the BS to a PDE and then uses what is called the "Heat equation" to get the final lognormal PDF. http://www.amazon.com/TheMathematicsF ... 0521497892 It goes into a lot of detail for these kinds of problems and if you are going to be doing this for a while you should get something like it. 

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black, finding, general, pde, scholes, solution 
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