In finance, economics, and decision theory, hyperbolic absolute risk aversion (HARA)[1]: p.39, [2]: p.389, [3][4][5][6] refers to a type of risk aversion that is particularly convenient to model mathematically and to obtain empirical predictions from. It refers specifically to a property of von Neumann–Morgenstern utility functions, which are typically functions of final wealth (or some related variable), and which describe a decision-maker's degree of satisfaction with the outcome for wealth. The final outcome for wealth is affected both by random variables and by decisions. Decision-makers are assumed to make their decisions (such as, for example, portfolio allocations) so as to maximize the expected value of the utility function.
Notable special cases of HARA utility functions include the quadratic utility function, the exponential utility function, and the isoelastic utility function.
^Ingersoll, Jonathan E. (1987). Theory of Financial Decision Making. Totowa, NJ: Rowman & Littlefield. ISBN 0847673596.
^Merton, Robert C. (1971). "Optimum Consumption and Portfolio Rules in a Continuous-Time Model". Journal of Economic Theory. 3 (4): 373–413. doi:10.1016/0022-0531(71)90038-X. hdl:1721.1/63980. (Chapter I of his Ph.D. dissertation; Chapter 5 in his Continuous-Time Finance).
^Mossin, Jan (1968). "Optimal multiperiod portfolio policies". Journal of Business. 41 (2): 215–229. doi:10.1086/295078. JSTOR 2351447.
^Ljungqvist & Sargent, Recursive Macroeconomic Theory, MIT Press, Second Edition
^Zender's lecture notes
^Carroll, C.D.; Kimball, M.S. (2008). "Precautionary saving and precautionary wealth". The New Palgrave Dictionary of Economics. CiteSeerX 10.1.1.67.7867.
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