The Pratt-Arrow Requirement in a Fourth Degree Polynomial Utility Function

1992 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Haskel Benishay
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Absolute Risk ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Absolute Risk Aversion

The main objective of this paper is to show that a fourth degree polynomial utility function proposed in a recent paper, which meets the requirement of risk aversion, can be restricted further to meet the added requirement of decreasing absolute risk aversion. Secondary objectives are to show the features and advantages of the proposed function.

BEHAVIORAL PORTFOLIO CHOICE UNDER HYPERBOLIC ABSOLUTE RISK AVERSION

2020 ◽  
Vol 23 (07) ◽  
pp. 2050045
Author(s):  
MARCOS ESCOBAR-ANEL ◽  
ANDREAS LICHTENSTERN ◽  
RUDI ZAGST
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Prospect Theory ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Absolute Risk ◽  
Investment Strategy ◽  
Absolute Risk Aversion ◽  
Distortion Functions ◽  
The Impact

This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.

Constant Absolute Risk Aversion, Bankruptcy, and Wealth-Dependent Decisions

1980 ◽  
Vol 53 (3) ◽  
pp. 285 ◽  
Author(s):  
Steven A. Lippman ◽  
John J. McCall ◽  
Wayne L. Winston
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Absolute Risk Aversion ◽  
Constant Absolute Risk Aversion

On the relationship between absolute prudence and absolute risk aversion

2006 ◽  
Vol 29 (2) ◽  
pp. 155-160 ◽  
Author(s):  
Mario A. Maggi ◽  
Umberto Magnani ◽  
Mario Menegatti
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Absolute Risk Aversion ◽  
The Relationship

DE FINETTI ON RISK AVERSION

2009 ◽  
Vol 25 (2) ◽  
pp. 153-159
Author(s):  
Joseph B. Kadane ◽  
Gaia Bellone
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Risk Premia ◽  
Absolute Risk Aversion ◽  
Kenneth Arrow ◽  
De Finetti ◽  
Constant Absolute Risk Aversion ◽  
Special Case

According to Mark Rubinstein (2006) ‘In 1952, anticipating Kenneth Arrow and John Pratt by over a decade, he [de Finetti] formulated the notion of absolute risk aversion, used it in connection with risk premia for small bets, and discussed the special case of constant absolute risk aversion.’ The purpose of this note is to ascertain the extent to which this is true, and at the same time, to correct certain minor errors that appear in de Finetti's work.

Fractional Degree Stochastic Dominance

2020 ◽  
Vol 66 (10) ◽  
pp. 4630-4647 ◽  
Author(s):  
Rachel J. Huang ◽  
Larry Y. Tzeng ◽  
Lin Zhao
Keyword(s):  
Lower Bound ◽  
Risk Aversion ◽  
Stochastic Dominance ◽  
Absolute Risk ◽  
Comparative Statics ◽  
Risk Averse ◽  
Absolute Risk Aversion ◽  
Risk Apportionment ◽  
Lottery Choices ◽  
Increase In Risk

We develop a continuum of stochastic dominance rules for expected utility maximizers. The new rules encompass the traditional integer-degree stochastic dominance; between adjacent integer degrees, they formulate the consensus of individuals whose absolute risk aversion at the corresponding integer degree has a negative lower bound. By extending the concept of “uniform risk aversion” previously proposed in the literature to high-order risk preferences, we interpret the fractionalized degree parameter as a benchmark individual relative to whom all considered individuals are uniformly no less risk averse in the lottery choices. The equivalent distribution conditions for the new rules are provided, and the fractional degree “increase in risk” is defined. We generalize the previously defined notion of “risk apportionment” and demonstrate its usefulness in characterizing comparative statics of risk changes in fractional degrees. This paper was accepted by David Simchi-Levi, decision analysis.

An Alternative Characterization of Decreasing Absolute Risk Aversion

Econometrica ◽  
1983 ◽  
Vol 51 (1) ◽  
pp. 223 ◽  
Author(s):  
Philip H. Dybvig ◽  
Steven A. Lippman
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Absolute Risk Aversion ◽  
Alternative Characterization
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