Conserved Densities of the Black-Scholes Equation

A class of new conserved densities of the Black-Scholes equation are constructed by using the multiplier that is derived from the result of divergence expression annihilation under the full Euler operator. The method does not depend on the symmetries of the Black-Scholes equation. These conserved densities can be expressed by solutions of the classical heat equation.     

AN OSCILLATION CRITERION FOR EVEN ORDER NEUTRAL DIFFERENCE EQUATIONS

An oscillation criterion is obtained for even order neutral type differenceequations of the following formΔ~m(x_n+α_nx_(n-т))+f(n,x_n,x_(n-σ))=0,n=n_0,n_0+1,…,where m≥2 is even, n_0 is a nonnegative integer, Δ is the forward differenceoperator defined by Δx_n=x_(n+1)-x_n, and for i≥1, Δ~i is the i~(th)-order forwarddifference operator defined by Δ~ix_n=Δ(Δ~(i-1)x_n),т and σ are positive integers.