Good-deal bounds
Encyclopedia
Good-deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if 
is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function 
by
where
is the set of final values for self-financing trading strategies. Then any price in the range 
does not provide a good deal for this trader, and this range is called the "no good-deal price bounds."
If
then the good-deal price bounds are the no-arbitrage price bounds, and correspond to the subhedging and superhedging price
s. The no-arbitrage bounds are the greatest extremes that good-deal bounds can take.
If
where 
is a utility function, then the good-deal price bounds correspond to the indifference price
bounds.
is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function bywhere
is the set of final values for self-financing trading strategies. Then any price in the range does not provide a good deal for this trader, and this range is called the "no good-deal price bounds."If
then the good-deal price bounds are the no-arbitrage price bounds, and correspond to the subhedging and superhedging priceSuperhedging price
The superhedging price is a coherent risk measure. The superhedging price of a portfolio is equivalent to the smallest amount necessary to be paid for a portfolio at the current time so that at some specified future time the value of B is at least as great as A...
s. The no-arbitrage bounds are the greatest extremes that good-deal bounds can take.
If
where is a utility function, then the good-deal price bounds correspond to the indifference priceIndifference price
In finance, indifference pricing is a method of pricing financial securities with regards to a utility function. Also known as the reservation price or private valuation. Particularly the indifference price is the price that an agent would have the same expected utility level between exercising a...
bounds.