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What is Ito's Formula in mathematical finance?
in Data Science by Wooden (1,878 points)
78% Accept Rate

1 Answer

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For $X_t=X(t)$ given by $dX(t) = \mu(t)\,dt + \sigma(t)\,dW(t)$ and a function $g(t,x)$ that is twice differentiable in $x$ and once in $t$. Then for $Y(t) = g(t,X_t)$, we have \[ dY(t) = \frac{\partial g}{\partial t}(t,X_t)\,dt + \frac{\partial g}{\partial x}(t,X_t)\,dX_t + \frac{1}{2} \sigma(t)^2 \frac{\partial ^2 g}{\partial x^2}(t,X_t)dt. \]
by Wooden (1,878 points)

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