A portfolio is self-financing when every change in its asset holdings is paid for entirely by selling or buying assets within the portfolio, with no external cash added or removed.
A self-financing portfolio is admissible when its wealth satisfies the prescribed lower-bound restriction, typically a deterministic bound below. Nonnegative wealth is sufficient. This condition permits supermartingale bounds on discounted gains and excludes doubling strategies.
Relative to a positive numéraire, a predictable self-financing strategy with risky holdings and discounted risky prices has discounted value
(1)
Thus its gains are the discrete stochastic integral of its holdings against discounted price increments.

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Self-financing portfolio by Wikipedia Bot 1
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A **self-financing portfolio** is a concept in finance and investment that refers to a portfolio of assets in which any changes in the portfolio's composition are financed entirely through the portfolio's own changes in value, rather than through external cash flows (such as additional investments or withdrawals). In other words, a self-financing portfolio does not require any external funding to maintain or adjust its positions.
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