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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 the individual can pay an amount of money $x$ so that she can avoid taking the bet (which leads to expected utility $75$). What's the maximum amount of money $x$ ...


7

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 the simple case of a household periodically re-balancing their investments in across both a fixed index fund and an equity index fund. The econometrician sees ...


7

"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 the gamble by $G$, a discrete uniform random variable taking three values according to the setup, we have $$U(CE) \equiv \sum_{i=1}^3p_iU(g_i) = E[U(G)] < ...


6

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 obtain an (approximate) equation for $R$. The expansion of first order on the RHS is motivated by this fact, i.e. to bring $R$ alone "in the surface". The ...


6

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) around 0.3-0.4. But it might also depend on what your goal is - the single parameter in CRRA utility controls both risk aversion and intertemporal smoothing ...


6

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 $$E[u_{RA}(N)] > E[u_{RA}(M)]$$ The fact that a risk-neutral agent ($RN$) could choose $M$ over $N$ implies that $$E[u_{RN}(N)] < E[u_{RN}(M)] \implies ...


5

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 causality, just a mathematical relationship. Risk aversion (risk preference) is not connected to discounting, which measures time preference. It does not make ...


5

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 Ninth International Congress of Logic, Methodology and Philosophy of Science. Harsanyi starts by proving the same lemma that Alecos proved in his answer, namely ...


4

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 optimal insurance scheme (such as the use of a mutual fund or a bank) flattens the yield curve. It is possible to show that the optimal portfolio problem solves: ...


4

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 regularity conditions, the coefficient of absolute risk aversion approximates the risk premium divided by half the variance for a small actuarily fair gamble. In ...


4

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 $\pi=\left(\pi_1,\pi_2,\dots,\pi_n\right)$. We can express this as the simple gamble: $$g = \left(\pi_1\circ w_1,\pi_2\circ w_2, \dots, \pi_n\circ w_n\right)$$ The ...


3

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. I would hope that no one claims that there is. The statistical value of life is a (somewhat lazy) calculation of convenience. Lots of business case protocols ...


3

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 aversion" does not mean what it means in everyday language. Being "risk averse" does not mean for the theory "I dislike risk", because taken literally "disliking ...


3

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 averse if, at any wealth level $w$, he or she dislikes every lottery $Z$ with an expected payoff of zero, $EZ = 0$, so that : $Eu(w + Z) =< u(w)$ Risk ...


3

Using the results derived in this answer we have the following relations for any utility function: (Absolute Risk Aversion = $A(c)$, Relative Risk Aversion = $R(c)$) : $$A(c) = -\frac {u''(c)}{u'(c)},\;\;\; R(c) = cA(c), \;\; A(c) = \frac 1c R(c)$$ and so $$\frac {\partial A(c)}{\partial c} = \frac {\partial [(1/c)R(c)]}{\partial c}= -\frac 1{c^2} R(c) ...


3

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 preferences fulfill DARA. If $c A(c)$ is constant, the preferences fulfill CRRA. If CRRA holds, then $A(c)$ must be decreasing in $c$. If we take any $A(c)$ such ...


3

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 not allowed...


3

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 mentioned in other answers expected utility is not equipped to handle uncertainty because it deals with taking expectations and expectations cannot be computed when ...


3

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 following table (the first column is the coefficient of absolute risk aversion) You can download the paper and trace the papers which it summarizes in the ...


3

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 risky (stochastic) and non risky assets and risk averse agents. For the thought experiment, we increase the volatility of the risky asset, "increasing its ...


3

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 $$E[u]=\frac{1}{2} u(100+125) + \frac{1}{2} u(100−100)= \frac{1}{2} u(225) =\frac{1}{2} \sqrt{225} = 7.5$$. By definition, the risk premium (R) must satisfy the ...


3

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, represents preference over lotteries of monetary outcomes. Thus, the argument of vNM utility is an object related to, but categorically distinct from, the object that ...


3

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 entrepreneurs. However, sensitivity analysis reveals that this result holds only for those individuals who were previously employed. For previously unemployed ...


3

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 and is indifferent to changes in variance A risk loving agent (RL) likes high mean and high variance From the fact that RN chooses $M$ over $N$, we known that ...


3

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 those domains. In the domain for gains, people are usually risk averse. However, in the domain for losses, people do tend to take larger risks. A nice ...


3

If you're willing to pay \$10 to reduce your risk of death by 1 in 1M, then your VSL is \$10M.† Example. Say there are two bike helmets. One costs \$20 while the other costs \$30. The two helmets are exactly identical, except that the more expensive one has been proven to reduce your risk of death by an additional 1 in 1M. If you're willing to buy the more ...


2

The lottery you show is equivalent to having two lotteries, one where you get \$50 with certainty and one with the following payoffs: \$0 with probability 1/3 \$50 with probability 1/3 \$100 with probability 1/3 The first lottery has a certainty equivalent of \$50. The second lottery has no negative payoffs and so shouldn't ever have a negative price. ...


2

In the Von Neumann-Morgenstern theory, arguments of the utility function are final consumption goods. The utility function is extended over lotteries by linearity but it does not really make sense to assume that the individual "consumes" the lotteries L1 and L2 in your scenario with the raffle tickets: what he ultimately consumes is the 100 dollars monetary ...


2

You want the household to be ex-ante indifferent between taking the lottery and paying some $p$ and voiding it. With van-Neumann-Morgenstein utility, the utility of taking the lottery is given by $$U_L(w) \equiv 0.5 U(w-1000) + 0.5U(w+1000)$$ Now, you're looking for a payment $p(w)$ such that $u(w - p(w)) = U_L(w)$.


2

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 described as "conditions"), that have to do with preferences/behavior of human beings. They may be given a strict mathematical expression (which is good), but they ...


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