= Investment-consumption arbitrage
An <investment-consumption arbitrage> is an admissible trading plan that starts with zero capital, withdraws nonnegative <consumption> at every date, and ends with no unpaid debt, with positive <consumption> occurring with positive <probability>. One may include final liquidation as the last <consumption> payment; equivalently require nonnegative terminal wealth and count its positive liquidation value.
The budget must be <self-financing> apart from these withdrawals: each withdrawal is funded by asset holdings, not by outside money. The terminal solvency condition is essential. Borrowing money, consuming it immediately and leaving a negative terminal balance is not an <arbitrage>. In a model with a positive <numéraire>, unused positive terminal wealth can be paid out as final <consumption>, connecting this definition to <pure-investment arbitrage>.
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