Self-financing portfolio

A self-financing portfolio is an important concept in financial mathematics.

A portfolio is self-financing if there is no exogenous infusion or withdrawal of money; the purchase of a new asset must be financed by the sale of an old one.

Let ${\displaystyle h_{i}(t)}$ denote the number of shares of stock number 'i' in the portfolio at time ${\displaystyle t}$, and ${\displaystyle S_{i}(t)}$ the price of stock number 'i' in a frictionless market with trading in continuous time. Let

${\displaystyle V(t)=\sum _{i=1}^{n}h_{i}(t)S_{i}(t).}$

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