Good–deal bounds are price bounds for a

financial portfolio In finance, a portfolio is a collection of investments. Definition The term "portfolio" refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial profess ...

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

\rho: \mathcal^p \to \mathbb

by :

\rho(X) = \inf\left\ = \inf\left\

where

A_T

is the set of final values for self-financing trading strategies. Then any price in the range

(-\rho(X), \rho(-X))

does not provide a good deal for this trader, and this range is called the "no good-deal price bounds." If

A = \left\

then the good-deal price bounds are the no-arbitrage price bounds, and correspond to the subhedging and

superhedging price The superhedging price is a coherent risk measure. The superhedging price of a portfolio (A) is equivalent to the smallest amount necessary to be paid for an admissible portfolio (B) at the current time so that at some specified future time the va ...

s. The no-arbitrage bounds are the greatest extremes that good-deal bounds can take. If

A = \left\

where

u

is a

utility function In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a Normative economics, normative context, utility refers to a goal or ob ...

, then the good-deal price bounds correspond to the

indifference price In finance, indifference pricing is a method of pricing financial securities with regard to a utility function. The indifference price is also known as the reservation price or private valuation. In particular, the indifference price is the pric ...

bounds.

References

Mathematical finance Pricing {{finance-stub