Portfolio Selection under Partial Observation and Constant Absolute Risk Aversion

2004 ◽  
Author(s):  
Simon Brendle
Keyword(s):  
Risk Aversion ◽  
Portfolio Selection ◽  
Absolute Risk ◽  
Partial Observation ◽  
Absolute Risk Aversion ◽  
Constant Absolute Risk Aversion

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

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.

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.

Portfolio Choice

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Choice Model ◽  
Absolute Risk ◽  
Risk Tolerance ◽  
Absolute Risk Aversion ◽  
Initial Wealth ◽  
Optimal Investments ◽  
Mean Variance ◽  
Constant Absolute Risk Aversion

The portfolio choice model is introduced, and the first‐order condition is derived. Properties of the demand for a single risky asset are derived from second‐order risk aversion and decreasing absolute risk aversion. Optimal investments are independent of initial wealth for investors with constant absolute risk aversion. Optimal investments are affine functions of initial wealth for investors iwth linear risk tolerance. The optimal portfolio for an investor with constant absolute risk aversion is derived when asset returns are normally distributed. Investors with quadratic utility have mean‐variance preferences, and investors have mean‐variance preferences when returns are elliptically distributed.

scholarly journals Short‐term investments and indices of risk

2020 ◽  
Vol 15 (3) ◽  
pp. 891-921
Author(s):  
Yuval Heller ◽  
Amnon Schreiber
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Risk Index ◽  
Decision Makers ◽  
Decision Problems ◽  
Risk Averse ◽  
Short Term ◽  
Risky Assets ◽  
Absolute Risk Aversion ◽  
Constant Absolute Risk Aversion

We study various decision problems regarding short‐term investments in risky assets whose returns evolve continuously in time. We show that in each problem, all risk‐averse decision makers have the same (problem‐dependent) ranking over short‐term risky assets. Moreover, in each problem, the ranking is represented by the same risk index as in the case of constant absolute risk aversion utility agents and normally distributed risky assets.

Utility and Risk Aversion

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Expected Utility ◽  
Absolute Risk ◽  
Risk Tolerance ◽  
Relative Risk Aversion ◽  
Absolute Risk Aversion ◽  
Certainty Equivalents ◽  
Conditional Expectations ◽  
Constant Absolute Risk Aversion

Expected utility is introduced. Risk aversion and its equivalence with concavity of the utility function (Jensen’s inequality) are explained. The concepts of relative risk aversion, absolute risk aversion, and risk tolerance are introduced. Certainty equivalents are defined. Expected utility is shown to imply second‐order risk aversion. Linear risk tolerance (hyperbolic absolute risk aversion), cautiousness parameters, constant relative risk aversion, and constant absolute risk aversion are described. Decreasing absolute risk aversion is shown to imply a preference for positive skewness. Preferences for kurtosis are discussed. Conditional expectations are introduced, and the law of iterated expectations is explained. Risk averse investors are shown to dislike mean‐independent noise.

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