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.

scholarly journals Long-Run Savings and Investment Strategy Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Russell Gerrard ◽  
Montserrat Guillén ◽  
Jens Perch Nielsen ◽  
Ana M. Pérez-Marín
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Investment Strategy ◽  
Maximum Amount ◽  
Constant Amount ◽  
Investment Performance ◽  
Risky Assets ◽  
Absolute Risk Aversion ◽  
Long Run ◽  
Life Cycle Savings

We focus on automatic strategies to optimize life cycle savings and investment. Classical optimal savings theory establishes that, given the level of risk aversion, a saver would keep the same relative amount invested in risky assets at any given time. We show that, when optimizing lifecycle investment, performance and risk assessment have to take into account the investor’s risk aversion and the maximum amount the investor could lose, simultaneously. When risk aversion and maximum possible loss are considered jointly, an optimal savings strategy is obtained, which follows from constant rather than relative absolute risk aversion. This result is fundamental to prove that if risk aversion and the maximum possible loss are both high, then holding a constant amount invested in the risky asset is optimal for a standard lifetime saving/pension process and outperforms some other simple strategies. Performance comparisons are based on downside risk-adjusted equivalence that is used in our illustration.

scholarly journals Design of Principal-agent Incentive Mechanism between Government and NPO

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Honglian Guo ◽  
Zhenzhen Wu ◽  
Han Li
Keyword(s):  
Risk Aversion ◽  
Expected Utility ◽  
Absolute Risk ◽  
Principal Agent ◽  
Output Level ◽  
Principal Agent Theory ◽  
Absolute Risk Aversion ◽  
Output Coefficient ◽  
The Impact ◽  
Society Research

Based on principal-agent theory, this paper establishes an incentive contract mechanism between government and NPO under asymmetric information, and analyzes the impact of absolute risk aversion and output level on the expected utility of government, NPO and society. Research shows that risk aversion is negatively correlated with the expected utility of government, NPO and society. The output coefficient is positively correlated with the expected utility of government, NPO and society. Reducing absolute risk aversion, increasing output coefficient and increasing government incentives can effectively motivate NPO to actively participate in social rescue activities.

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.

scholarly journals Closed-Form Optimal Strategies of Continuous-Time Options with Stochastic Differential Equations

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Wei Yan
Keyword(s):  
Differential Equations ◽  
Risk Aversion ◽  
Utility Function ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Absolute Risk ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Hara Utility

A continuous-time portfolio selection with options based on risk aversion utility function in financial market is studied. The different price between sale and purchase of options is introduced in this paper. The optimal investment-consumption problem is formulated as a continuous-time mathematical model with stochastic differential equations. The prices processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman (HJB) equation of the problem is represented and its solution is obtained in different conditions. The above results are applied to a special case under a Hyperbolic Absolute Risk Aversion (HARA) utility function. The optimal investment-consumption strategies about HARA utility function are also derived. Finally, an example and some discussions illustrating these results are also presented.

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
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