Re: help with pde

*To*: mathgroup at smc.vnet.net*Subject*: [mg16151] Re: help with pde*From*: "Lawrence A. Walker Jr." <lwalker701 at earthlink.net>*Date*: Sat, 27 Feb 1999 03:23:13 -0500*Organization*: Morgan State University*References*: <7b357t$21s@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I don't know of an automatic way of doing it. I never got a chance to check this out but I think that in order to solve it you must: 1. Take the Laplace transform of the equation to change t into another variable. 2. Now we have a 2nd order DE in LaplaceTransform[V[s,t],t,s], so we can solve this automatically or take the fouier transform, then apply the inverse fouier after algebraically manipulating the equation. 3. Take the inverse LaplaceTransform. Take Care, Lawrence Will Holt wrote: > Hi everyone, > > I am trying to solve the Black-Scholes pde in mathematica subject to the > usual boundary conditions. > > 0.5*sigma[0]^2*S^2*D[V[S,t],S,S]+r[0]*S*D[V[S,t],S]-r[0]*V[S,t]+*D[V[S,t],t] > =0 > > V[0,T]=0,V[S,T]=Max[S-K,0], for some particular S[0], K and T. > > The Mathematica command "NDSolve" requires that the first argument must have > both an equation and an initial condition. > The problem is that the law motion for S is > > dS=alpha[0]*S*dt+sigma[0]dZ > > where dZ is a Wiener process that can be substituted by epsilon*SQRt[dt], > with epsilon a random drawing from a standardised normal distribution. > > I thought that I did not have to include this law motion for S in NDSolve, > but in case I do have to include it, how can I do this? > > Also, on a different issue, how can I generate three series of normal random > numbers that are correlated amongst each other: rho12, rho23, rho13? e.g. > dX1=rho12dX2+SQRT[1-rho12^2]*de12, with de12 a standard Wiener process > independent of dX2, and so on for dX2 and dX3. > > Any help will be greatly appreciated. > > Will.