9 votes
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Risk Premium in the Expected Utility Theory

Is there any (economic) rational for the first-order expansion of the RHS? And for its different neighborhood evaluation? As for your first question: This is a purely mathematical tactic in order to ...
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9 votes
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Intuition behind risk premium

The name for the amount $56.25 is certainty equivalent. The expected utility for the individual from taking the bet is calculated as follows: $$E[U]=\frac12U(100+125)+\frac12U(100-100)=75$$ Suppose ...
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7 votes
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given someone's past investing history, is there a way to calculate his risk aversion?

Generally speaking no. You wouldn't be able to distinguish re-balancing for risk aversion reasons from re-balancing motivated by changes in expected returns or the co-variance of returns. Consider ...
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7 votes
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Can a risk-averse agent's Certainty Equivalent be lower than the lowest possible outcome of a gamble?

"Since agent is risk averse, we would expect that $U(E[g]) < U(CE)$ , where $CE$ is the certainty equivalent." This is wrong. I presume the Expected Utility Property holds here, so, if we denote ...
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6 votes
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Does risk aversion cause diminishing marginal utility, or vice versa?

I think I've found an answer to my question, in this excerpt from Nobel laureate John C. Harsanyi's 1994 paper "Normative validity and meaning of von neumann-morgenstern utilities", presented at the ...
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6 votes

Empirical estimates of CRRA and CARA utility

There are many estimates in the literature. For example, Havranek (2013) does a meta-analysis of avalible results and argues for a value of intertemporal elasticity (inverse of sigma in your notation) ...
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6 votes

a risk lover agent preferences and the preference of risk natural agent may be the same

Don't commit the cardinal mistake of equating preferences with choices. In the context of Expected Utility Theory, the fact that a risk-averse agent ($RA$) would choose $N$ over $M$ implies that $...
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5 votes

Does risk aversion cause diminishing marginal utility, or vice versa?

The utility function is a representation of preferences, which are traditionally inferred from choices. Preferences come before utility. I would not call the connection between utility and preferences ...
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5 votes
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Why is the risk premium always positive for risk averse individuals?

Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(...
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4 votes

Intuition behind risk premium

There is a typo in the figure that introduces some confusion in the previous answer, which is basically wrong. Based on the numbers and the figure, the utility is such that $$u=\sqrt{x},$$ so $$E[u]=\...
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4 votes
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What behaviour do different values of Relative Risk Aversion imply?

In the D&D model, We deal with a 2 periods economy where the agent can invest in a short term project that yields $0$ or a long term project that yields $R$; It is possible to prove that an ...
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4 votes
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Derivation of Arrow-Pratt risk aversion measure

Please find below the pages which may interest you. Arrow, K. J. Essays in the Theory of Risk-Bearing, North-Holland Publishing Company, 1971 I let the admin delete this post if the few extracts are ...
4 votes

Does decreasing marginal utility imply risk aversion?

What you are misunderstanding, is that in expected utility theory, marginal utility is not an independent concept from "risk aversion", as the latter is defined in the context of that theory: "risk ...
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4 votes

Risk Premium in the Expected Utility Theory

It is worth noting that the "risk premium" you are talking about is in fact more accurately referred to as the Arrow-Pratt approximation of the cost of a small additive risk. You can approximate it ...
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4 votes

Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

Yes, there is such an interpretation in Section 3 of the original paper by Pratt: Pratt, J. (1964). Risk Aversion in the Small and in the Large. Econometrica, 32(1/2), 122-136. Under some ...
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4 votes

Why is the Marginal Utility of losses deminishing in Prospect Theory?

The value function used in Kahneman's prospect theory (which your plot shows) is supposed to capture empirically observed behavior of people's attitudes towards gains/losses as well as to risks in ...
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4 votes

Examples of risk-neutral firms or people in business

Its very hard to give an actual real world example of risk neutral person (firms are just run by people only people can have attitudes to risk) not because they do not exist but because research on ...
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3 votes

Negative expected value; risk neutral choice

There are three type of individuals : risk averse, risk neutral and risk loving. Individuals evaluate risky prospects such as to maximize the expected level of their utility. So, an agent is risk ...
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3 votes
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Is DARA utility implying CRRA most of the time?

Using the results derived in this answer we have the following relations for any utility function: (Absolute Risk Aversion = $A(c)$, Relative Risk Aversion = $R(c)$) : $$A(c) = -\frac {u''(c)}{u'(c)...
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3 votes

Is DARA utility implying CRRA most of the time?

Let me turn my comment into a quick answer: Using the notation of the article you quoted $A(c)$ is the absolute risk aversion and $c A(c)$ the relative risk aversion. If $A(c)$ is decreasing, the ...
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3 votes

Why should the statistical value of life exist?

You asked: why should there exist a single value of $X$ that satisfies this definition for all values of $p$, or even all values of $p$ that are sufficiently close to $0$ There isn't such a value....
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3 votes

Does risk aversion cause diminishing marginal utility, or vice versa?

The Expected Utility property is not a property that depends on the functional form of the utility function. Its existence depends on satisfying certain "axioms" (which would be more acurately be ...
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3 votes

Question about the Ellsberg Paradox in Expected Utility Theory

The short answer seems to be yes your example violates expected utility... It mostly seems to me like a simple transformation of the first example you gave (but you got rid of the red balls). As ...
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  • 1,563
3 votes
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Empirical estimates of CRRA and CARA utility

In Babcock, B. A., Choi, E. K., & Feinerman, E. (1993). Risk and probability premiums for CARA utility functions. Journal of Agricultural and Resource Economics, 17-24. (downloadable) we find the ...
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3 votes

Does risk aversion of utility function cause the existence of positive interest rate?

Yes and no; it depends on which interest rate you look at. You are right in that risk aversion affects interest rates, but the direction can go both ways. In what follows I look at an economy with ...
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3 votes
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von-Neumann-Morgenstern v. Bernoulli Utility Function

Bernoulli utility represents preference over monetary outcomes. In a way, this is no different from the typical utility functions defined over consumption bundles. vNM utility, in contrast, ...
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3 votes
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Entrepreneurs and risk aversion

Interestingly—and much in contrast to recent research—our data supports the conventional wisdom that persons with a higher inclination towards risk have a significantly higher probability of becoming ...
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3 votes
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a risk lover agent preferences and the preference of risk natural agent may be the same

Another way of looking at this problem is to consider the means and variances of the lotteries. A risk averse agent (RA) likes high mean and low variance A risk neutral agent (RN) likes high mean ...
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  • 14.4k
3 votes
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Construct utility function for a risk-averse agent

If $-|x-a|$ represents the monetary payoff associated with the policy choice $a$, then $u(a) =-\left(|x-a|^\gamma\right)$ is risk averse for $\gamma > 1$, and risk loving for $0<\gamma < 1$.
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