HARA Utility

Definition

HARA (Hyperbolic Absolute Risk Aversion) is a family of utility functions used in financial decision-making to model how people value wealth under risk.

A common form/example is:

$$U(x)=\frac{(x-F{)}^a}{a}$$

where

• $x$ = final wealth
• $F$ = subsistence / disaster level (ruin threshold)
• $a$ = risk-aversion parameter

HARA models the idea that people become more risk-average as they approach financial ruin, and more risk-tolerant as they become wealthier.

Special Cases

For the function above, there are many ways to choose our parameters $a$ and $F$.

Parameters	Result
$a=1$	Linear utility (risk-neutral)
$a\to 0$	Log utility (Kelly criterion)
$F=0$	Power / CRRA utility
$F\ne 0$	True HARA (ruin-aware)

Interpretating