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Itô's Lemma


\begin{displaymath}
V_t-V_0 = \int_0^t f_x(S_u, T-u)\,dS_u-\int_0^t f_\tau(S_u, ...
...xtstyle{1\over 2}}\sigma^2\int_0^t {S_u}^2f_{xx}(S_u,T-u)\,du,
\end{displaymath}

where $V_t=f(S_t,\tau)$ for $0\leq\tau\equiv T-t\leq T$, and $f\in C^{2,1}((0,\infty)\times [0,T])$.


References

Price, J. F. ``Optional Mathematics is Not Optional.'' Not. Amer. Math. Soc. 43, 964-971, 1996.




© 1996-9 Eric W. Weisstein
1999-05-26