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risk aversion is a hyperbola, namely

:

The solution to this differential equation (omitting additive and multiplicative constant terms, which do not affect the behavior implied by the utility function) is:

:

where and .Note that when , this is CARA, as , and when , this is CRRA (see below), as .See
* Decreasing/increasing absolute risk aversion (DARA/IARA) is present if is decreasing/increasing. Using the above definition of ARA, the following inequality holds for DARA:

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