Indifference price
Encyclopedia
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 financial transaction
and not (with optimal trading otherwise). Typically the indifference price is a pricing range (a bid-ask spread) for a specific agent, this price range is an example of good-deal bounds.
and a claim 
with known payoffs at some terminal time 
. If we let the function 
be defined by
where
is the initial endowment, 
is the set of all self-financing portfolio
s at time
starting with endowment 
, and 
is the number of the claim to be purchased (or sold). Then the indifference bid price 
for 
units of 
is the solution of 
and the indifference ask price 
is the solution of 
. The indifference price bound is the range 
.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, indifference pricing is a method of pricing financial securities with regards to a utility function. Also known as the reservation price
Reservation price
In microeconomics, the reservation price is the highest price a buyer is willing to pay for goods or a service; or; the smallest price at which a seller is willing to sell a good or service...
or private valuation. Particularly the indifference price is the price that an agent would have the same expected utility level between exercising a financial transaction
Financial transaction
A financial transaction is an event or condition under the contract between a buyer and a seller to exchange an asset for payment. It involves a change in the status of the finances of two or more businesses or individuals.-History:...
and not (with optimal trading otherwise). Typically the indifference price is a pricing range (a bid-ask spread) for a specific agent, this price range is an example of good-deal bounds.
Mathematics
Given a utility function and a claim with known payoffs at some terminal time . If we let the function be defined by
-
,
where
is the initial endowment, is the set of all self-financing portfolioSelf-financing portfolio
Self-financing portfolio, an important concept in financial mathematics.A portfolio is self-financing if there is no exogenous infusion or withdrawal of money; the purchase of a new asset must be financed by the sale of an old one.- Mathematical definition :...
s at time
starting with endowment , and is the number of the claim to be purchased (or sold). Then the indifference bid price for units of is the solution of and the indifference ask price is the solution of . The indifference price bound is the range .