In
finance
Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...
, indifference pricing is a method of pricing
financial securities
A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
with regard to a
utility function
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosopher ...
. The indifference price is also known as the
reservation price
In economics, a reservation (or reserve) price is a limit on the price of a good or a service. On the demand side, it is the highest price that a buyer is willing to pay; on the supply side, it is the lowest price a seller is willing to accept ...
or private valuation. In particular, the indifference price is the price at which an agent would have the same
expected utility The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
level by exercising a
financial transaction
A financial transaction is an agreement, or communication, between a buyer and seller to exchange goods, services, or assets for payment. Any transaction involves a change in the status of the finances of two or more businesses or individuals. A ...
as by not doing so (with optimal trading otherwise). Typically the indifference price is a pricing range (a
bid–ask spread
The bid–ask spread (also bid–offer or bid/ask and buy/sell in the case of a market maker) is the difference between the prices quoted (either by a single market maker or in a limit order book) for an immediate sale (ask) and an immediate pur ...
) 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
let the function
be defined by
: