Suvarna Garge (Editor)

Good–deal bounds

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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.

References

Good–deal bounds Wikipedia