Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if A is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function ρ : L p → R by
ρ ( X ) = inf { t ∈ R : ∃ V T ∈ A T : X + t + V T ∈ A } = inf { t ∈ R : X + t ∈ A − A T } where A T is the set of final values for self-financing trading strategies. Then any price in the range ( − ρ ( X ) , ρ ( − X ) ) does not provide a good deal for this trader, and this range is called the "no good-deal price bounds."
If A = { Z ∈ L 0 : Z ≥ 0 P − a . s . } then the good-deal price bounds are the no-arbitrage price bounds, and correspond to the subhedging and superhedging prices. The no-arbitrage bounds are the greatest extremes that good-deal bounds can take.
If A = { Z ∈ L 0 : E [ u ( Z ) ] ≥ E [ u ( 0 ) ] } where u is a utility function, then the good-deal price bounds correspond to the indifference price bounds.
