Good-deal bounds

Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if ${\displaystyle A}$ is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function ${\displaystyle \rho :{\mathcal {L}}^{p}\to \mathbb {R} }$ by

where ${\displaystyle A_{T}}$ is the set of final values for self-financing trading strategies. Then any price in the range ${\displaystyle (-\rho (X),\rho (-X))}$ does not provide a good deal for this trader, and this range is called the "no good-deal price bounds."

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