![]() This is iso- because this kind of utility function leads to identical (or at least proportionate) decisions: it means that the optimal risk/reward behaviour at given level of wealth $w$ is also optimal for another level of wealth $kw$ if you multiply all the original investments by $k$. In the case of a power or log utility, this. This function captures the notion of risk aversion, which is the concept that an individual is willing to pay a premium to avoid risk. The ArrowPratt index of risk aversion is defined by. The power utility function, u(w)1/(1)w(1), is a commonly used utility function for representing the preferences of an individual when faced with a financial decision. The value represents log utility and represents a power utility function of the form. This article is a self-contained survey of utility functions and some of their applications. You can change the utility function using the risk aversion parameter. ![]() an affine transformation of the original utility function The first graph shows the utility function used. ![]() Iso-elastic utility is defined as a function $U(w)$ where for all $k \gt 0$ you have $$U(kw)=f(k)U(w)+g(k)$$ for some functions $f(k)$ and $g(k)$ independent of $w$, i.e. The power family, also known as the family of constant relative risk aversion (CRRA), is the most widely used parametric family for fitting utility functions to data. In fact, depending on the choice of the expo-power utility function parameters, we cover a diverse range of utility functions. ![]()
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