90 Frequently Asked Questions In Quantitative Finance
What is a Utility Function and How is
it Used?
Short Answer
A utility function represents the ‘worth,’ ‘happiness’ or
‘satisfaction’ associated with goods, services, events,
outcomes, levels of wealth, etc. It can be used to rank
outcomes, to aggregate ‘happiness’ across individuals
and to value games of chance.
Example
You own a valuable work of art, you are going to put
it up for auction. You don’t know how much you will
make but the auctioneer has estimated the chances of
achieving certain amounts. Someone then offers you a
guaranteed amount provided you withdraw the painting
from the auction. Should you take the offer or take your
chances? Utility theory can help you make that decision.
Long Answer
The idea is not often used in practice in finance but
is common in the literature, especially economics lit-
erature. Theutility functionallows the ranking of the
otherwise incomparable, and is used to explain people’s
actions; rational people are supposed to act so as to
increase their utility.
When a meaningful numerical value is used to represent
utility this is calledcardinal utility. One can then talk
about one thing having three times the utility of another,
and one can compare utility from person to person. If
the ordering of utility is all that matters (so that one
is only concerned with ranking of preferences, not the
numerical value) then this is calledordinal utility.
If we denote a utility function byU(W)whereWis
the ‘wealth,’ then one would expect utility functions to
