Partial Differential Equations in Finance

Abstract

Let u be a function of several real variables (t, x ₁, x ₂, …, x _n ):

$$ \begin{gathered} u:\mathbb{R}^ + \times \mathbb{R}^n \quad \,\, \to \mathbb{R} \hfill \\ \left( {t,x_1 ,x_2 , \ldots ,x_n } \right) \mapsto u\left( {t,x_1 ,x_2 , \ldots ,x_n } \right) \hfill \\ \end{gathered} $$