October 7th, 2003, 7:20 am
I am looking in "Mathematical Methods for Foreign Exchange" by Alexander Lipton, p 377. I have a question about the derivation of one of the boundary conditions, he says that for v -> infinity we need to have all the terms proportional to v to disappear,C_t - .5vS^2C_SS - epsilon rho v S C_Sv - .5epsilon^2 v C_vv - rSC_S - kappa(theta-v)C_v + rC =0this sounds reasonable to me,ie -v(.5S^2C_SS + epsilon rho S C_Sv + .5epsilon^2 C_vv - kappa C_v) = 0and then concludes that C=aS + b for large v, ie it is a linear function in S.Could it have equally been said thatlim v(.5S^2C_SS + epsilon rho S C_Sv + .5epsilon^2 C_vv- kappa C_v) = Kv->infinitywhere K is a constant is OK as well? CheersTony