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In finance, economics, and decision theory, hyperbolic absolute risk aversion (HARA)〔 (Chapter I of his Ph.D. dissertation; Chapter 5 in his ''Continuous-Time Finance'').〕〔Ljungqvist & Sargent, Recursive Macroeconomic Theory, MIT Press, Second Edition〕 〔(Zender's lecture notes )〕 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. ==Definition== A utility function is said to exhibit hyperbolic absolute risk aversion if and only if the level of risk tolerance —the reciprocal of absolute risk aversion —is a linear function of wealth ''W'': : where ''A''(''W'') is defined as –''U "''(''W'') / ''U'' '(''W''). A utility function ''U''(''W'') has this property, and thus is a HARA utility function, if and only if it has the form : with restrictions on wealth and the parameters such that and For a given parametrization, this restriction puts a lower bound on ''W'' if and an upper bound on ''W'' if . For the limiting case as → 1, L'Hôpital's rule shows that the utility function becomes linear in wealth; and for the limiting case as goes to 0, the utility function becomes logarithmic: . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hyperbolic absolute risk aversion」の詳細全文を読む スポンサード リンク
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