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.

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.

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.

scholarly journals Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Christian Gollier
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Interest Rates ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Absolute Risk ◽  
Second Order ◽  
Relative Risk Aversion ◽  
Portfolio Risk ◽  
First Order

We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.

scholarly journals AN ECONOMIC RISK ANALYSIS OF WEED-SUPPRESSIVE RICE CULTIVARS IN CONVENTIONAL RICE PRODUCTION

2018 ◽  
Vol 50 (4) ◽  
pp. 478-502 ◽  
Author(s):  
K. BRADLEY WATKINS ◽  
DAVID R. GEALY ◽  
MERLE M. ANDERS ◽  
RANJITSINH U. MANE
Keyword(s):  
Risk Analysis ◽  
Risk Aversion ◽  
Absolute Risk ◽  
Rice Production ◽  
Risk Averse ◽  
Rice Cultivars ◽  
Economic Risk ◽  
Absolute Risk Aversion ◽  
Certainty Equivalents

AbstractWeed-suppressive rice cultivars have the potential to reduce heavy reliance on synthetic herbicides in rice production. However, the economics of using weed-suppressive rice cultivars in conventional rice systems have not been fully evaluated. This study uses simulation and stochastic efficiency with respect to a function to rank weed-suppressive and weed-nonsuppressive rice cultivars under alternative herbicide intensity levels based on their certainty equivalents mapped across increasing levels of absolute risk aversion. The results indicate risk-averse rice producers would prefer to grow weed-suppressive cultivars using less herbicide inputs than what would be used to grow weed-nonsuppressive rice cultivars.

scholarly journals Calculation of Price Equilibria for Utility Functions of the HARA Class

1986 ◽  
Vol 16 (S1) ◽  
pp. S91-S97 ◽  
Author(s):  
Markus Lienhard
Keyword(s):  
Risk Aversion ◽  
Expected Utility ◽  
Closed System ◽  
Absolute Risk ◽  
Utility Functions ◽  
The Other ◽  
Pareto Optimum ◽  
Price Equilibrium ◽  
Absolute Risk Aversion ◽  
The One

AbstractWe explicitly calculate price equilibria for power and logarithmic utility functions which—together with the exponential utility functions—form the so-called HARA (Hyperbolic Absolute Risk Aversion) class.A price equilibrium is economically admissible in the market which is a closed system. Furthermore it is on the one side individually optimal for each participant of the market (in the sense of maximal expected utility), on the other side it is a Pareto optimum and thus collectively optimal for the market as a whole.

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.

scholarly journals The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Chunhua Hu ◽  
Wenyi Huang ◽  
Tianhao Xie
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Discrete Time ◽  
Rational Expectation ◽  
Absolute Risk ◽  
Wealth Distribution ◽  
Optimal Solution ◽  
Distribution Model ◽  
Relative Risk Aversion ◽  
Time Domains

A wealth distribution model on isolated discrete time domains, which allows the wealth to exchange at irregular time intervals, is used to describe the effect of agent’s trading behavior on wealth distribution. We assume that the agents have different degrees of risk aversion. The hyperbolic absolute risk aversion (HARA) utility function is employed to describe the degrees of risk aversion of agents, including decreasing relative risk aversion (DRRA), increasing relative risk aversion (IRRA), and constant relative risk aversion (CRRA). The effect of agent’s expectation on wealth distribution is taken into account in our wealth distribution model, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth status. The Euler equation and transversality condition for the model on isolated discrete time domains are given to prove the existence of the optimal solution of the model. The optimal solution of the wealth distribution model is obtained by using the method of solving the rational expectation model on isolated discrete time domains. A numerical example is given to highlight the advantages of the wealth distribution model.

Sign in / Sign up

Export Citation Format

Share Document