Ito Lemma
Tags: #Financial #EconomicsEquation
$$\mathrm{d}X(t) = a(t, X(t)) \mathrm{d}t + b(t, X(t))\mathrm{d} Z(t) \\ Y(t) = f(t, X(t)) \mathrm{d}t \\ \mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\mathrm{d} X(t) + \frac{1}{2} f_{xx}(t, X(t))[\mathrm{d}X(t)]^{2} \\ [\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\mathrm{d} t$$Latex Code
\mathrm{d}X(t) = a(t, X(t)) \mathrm{d}t + b(t, X(t))\mathrm{d} Z(t) \\
Y(t) = f(t, X(t)) \mathrm{d}t \\
\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\mathrm{d} X(t) + \frac{1}{2} f_{xx}(t, X(t))[\mathrm{d}X(t)]^{2} \\
[\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\mathrm{d} t
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Introduction
Equation
Latex Code
\mathrm{d}X(t) = a(t, X(t)) \mathrm{d}t + b(t, X(t))\mathrm{d} Z(t) \\
Y(t) = f(t, X(t)) \mathrm{d}t \\
\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\mathrm{d} X(t) + \frac{1}{2} f_{xx}(t, X(t))[\mathrm{d}X(t)]^{2} \\
[\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\mathrm{d} t
Explanation
Latex code for the Ito Lemma.
: Diffusion
: Stochastic differential equation for X(t)
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