HARA preferences details

The paper Optimum consumption and portfolio rules in a continuous-time model (Merton (1971)) presents (as far as I know, the initial presentation.

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Next we turn to a paper that discusses the importance of the HARA utility. The Fundamental Nature of HARA Utility (Perets and Yashiv (2013))

Many models in Economics assume a utility function belonging to the HARA family. This paper shows that HARA utility is fundamental to economic analysis. The HARA functional form is the unique form which satisfies basic economic principles in an optimization context. Using HARA is not just a matter of convenience or tractability but rather an essential restriction....

This notable paper has a multi page exploration of the HARA utility family. Implications of Constant Risk Aversion (Bamberg and Spremann (1981))

The assumption of constant risk aversion often leads to a considerable simplification of decision theoretic analyses. It is shown that this restriction on constant risk aversion permits the description of a wide range of risk averse patterns between the extreme cases of risk neutrality and the exclusive orientation on the pessimistic maxmin criterion. In particular, a new axiomatic foundation of the constant risk aversion is given and a series of properties for the certainty equivalent are derived. Possible applications are shown by the treatment of risk premiums, values of information, portfolio selection, capital market theory and syndicates.

There is a book that I can't vouch for but may be useful: Hyperbolic absolute risk aversion: Second Edition