Should the "value function" be "utility function" in prospect theory?
The terminology in microeconomics is not completely unified but typically differs slightly from the mathematical one. For a real-valued random (outcome) variable $X$, the mathematical expected value $\mathbb{E}(X)$ would rather be called the expectation of $X$. The utility $u(x)$ of an outcome $x$ is understood to be given by a (Bernoulli) utility function in the sense of EUT, i.e. a function $u(.)$ such that the expected utility $\mathbb{E}(u(.))$, sometimes written as a (von-Neumann-Morgenstern) utility function $U(.)$ on lotteries on outcomes, represents the preferences over lotteries on outcomes, while in behavioral economics the term value or valuation $v(x)$ typically represents some kind of subjective valuation of $x$, as e.g. in prospect theory. (So here, value is not to be understood as the mere numerical value of $x$, as in the usual mathematical definition of a &quot;function value&quot; or an &quot;expected value&quot;.)
Confusingly, however, $v(.)$ is sometimes also used to denote an alternative (Bernoulli) utility function. For example when explaining that a positive linear transformation of a utility function is again a utility function representing the same preferences, one of them is usually denoted by $u$ and the other by $v$. Moreover, in a utilitarian framework, $v(.)$ is often used to denote the willingness to pay for $x$, i.e. a monetary valuation of $x$.