11 votes

What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?

Well there is no opinion poll among economists on specifically this problem, but what can be judged from reaction of economists the consensus is that the Ole Peters paper is misguided and irrelevant ...
1muflon1's user avatar
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10 votes

An agent's expected utility depends only on mean and variance

In order to understand this problem, I will work through the generic case. Say that a user had generalized quadratic (Bernoulli) utility, similar to your problem: $$u(x) = \beta x^2 + \gamma x$$ and ...
Kitsune Cavalry's user avatar
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9 votes
Accepted

An agent's expected utility depends only on mean and variance

\begin{eqnarray*} \displaystyle U(L) & = &\sum_{s=1}^{S}\pi_s U(Y_s) = \sum_{s=1}^{S} \left(-\frac{1}{2}\pi_s(\alpha - Y_s)^2\right) = -\frac{1}{2}\sum_{s=1}^{S} \left(\pi_s(\alpha^2 + Y_s^2-2\...
Amit's user avatar
  • 8,411
8 votes

What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?

Junior econ professor here. I saw Ole Peter's work and I was intrigued, so I actually looked into it to see if there was something original/insightful for me to learn. I even run a little simulation ...
bbecon's user avatar
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8 votes

What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?

I’am the guy who wrote the short note that was mentioned in the original question. You can reach the note here. https://osf.io/preprints/socarxiv/axkfg/ I got interested in Peter's paper because of my ...
Luciano Andreozzi's user avatar
7 votes
Accepted

Envelope Paradox

Here is an "expected utility maximization/ game theoretic" approach to the matter (with a dash of set-theoretic probability). In such a framework, the answers appear clear. PREMISES We are told in ...
Alecos Papadopoulos's user avatar
7 votes
Accepted

Meaning of $dF(z)$ in expected utility framework

Not all cdf’s have a density function, (for example if $F$ is not differentiable). However, when they do have a density, the notation $dF(z)$ is equivalent to $f(z)dz$. When performing integrals. ...
Regio's user avatar
  • 4,188
6 votes

How does expected utility theory treat losses?

Gains and losses presuppose a reference point, which is not a feature in standard expected utility theory. In this theory, the only argument in the utility over wealth is $w$, the absolute level of ...
Herr K.'s user avatar
  • 15.4k
6 votes

Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Many people accept the axiomatizations of expected utility as normatively appealing, especially in contexts of pure risk. For people with this view, rational decision-makers should behave in ...
Michael Greinecker's user avatar
6 votes
Accepted

Expected value inside a utility function

No, $u_1(x_1-E[x_2])$ is agent $1$'s utility of the expected value, not the expected utility of the value. Generally $u(E(x)) \neq E(u(x))$. A simple example: Let $x$ take value $-1$ with probability $...
Giskard's user avatar
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5 votes

Experiments contradicting the expected utility model

Picking up my comment under this answer. One striking issue relevant to decisions not captured by expected utility is the framing effect discussed by Tversky and Kahneman (1981) and others. In their ...
Bayesian's user avatar
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5 votes
Accepted

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(...
lunar_props's user avatar
5 votes
Accepted

Who is the first one to equate "rational" with "complete and transitive preference"?

As pointed in the comments this was done by Ragnar Frisch. At least Barten and Böhm. (1982) as well as Johansen (1969) attribute these axioms to one of these two publications: Frisch, Ragnar (...
1muflon1's user avatar
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5 votes
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Expected utility theory (Lottery notation)

$$ \left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right) $$ is the lottery where you get $1000$ with probability $2/100$ and $0$ with probability $98/100$. The expression $$ 20 \sim \left(...
tdm's user avatar
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4 votes

Experiments contradicting the expected utility model

Let me mention another quite well-known one: The calibration theorem by Rabin (2000) and Rabin and Thaler (2002). The idea is that over small stakes individuals must be essentially risk-averse, but in ...
Bayesian's user avatar
  • 5,280
4 votes

Have there been attempts to measure the value of specific taught skills?

Have there been any empirical attempts to estimate the value of being taught specific skills - for example, phonics or solving algebraic equations? If I may be brazen enough to challenge the basis of ...
EconJohn's user avatar
  • 8,305
4 votes
Accepted

Maximal Allais paradox

One must first distinguish two different senses in which the Allais Paradox can be seen as a "contradiction" of vNM independence; these correspond to the two different interpretations which can be ...
Marcus Pivato's user avatar
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 ...
Michael Greinecker's user avatar
4 votes

Modelling Bounded Utility Functions

There are many such utility functions. Most commonly: \begin{equation} u(x)=L-\mathrm e^{-ax},\tag{1} \end{equation} where typically $a>0$. Or \begin{equation} u(x)=L-(x-a)^2.\tag{2} \end{...
Herr K.'s user avatar
  • 15.4k
4 votes

What are some non-von-Neumann-Morgenstern preferences used in economics?

The von Neumann-Morgenstern (vNM) utility function takes the form \begin{equation} U(p,x)=\sum_{i=1}^np_iu(x_i) \end{equation} where $x=(x_1,\dots,x_n)$ with $x_i$ being the (monetary) payoff ...
Herr K.'s user avatar
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4 votes
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Lotteries and expected utility

Your example is the classic Allais paradox. I think the best way to see how the preference pattern $L_1\succ L_2$ and $L_3\succ L_4$ violates independence is to visualize it geometrically. Consider ...
Herr K.'s user avatar
  • 15.4k
4 votes

Why can we write any lottery as a convex combination of the degenerate lotteries?

Pick any set of non-negative $p_1,\dots,p_n$ such that $p_1+\cdots+p_n=1$. The convex combination of degenerate lotteries $L^1,\dots,L^n$ with the $p_i$'s can be written as \begin{align} p_1L^1+\...
Herr K.'s user avatar
  • 15.4k
4 votes

The efficient frontier in mean variance criterion

Using $\mathbb E$ for the expected value symbol, $E_R$ and $V_R$ for the mean and the avriance of returns $R$, for a utility function of the form $$U(R) = \ln(1+R)$$ the second-order Taylor expansion ...
Alecos Papadopoulos's user avatar
4 votes
Accepted

Why utility rather than expected utility in Cochrane's "Asset Pricing"?

As mentioned in the comments this comes down to stylistic choices, since as you correctly pointed out: $$u(c_t)+\beta E_t[u(c_{t+1})]=E_t[u(c_t)+\beta u(c_{t+1})]$$ However, in principle both ...
1muflon1's user avatar
  • 55.6k
4 votes

Comparing & contrasting decision problems and normal games

Decision under uncertainty is sometimes called a "game against chance", and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states ...
Herr K.'s user avatar
  • 15.4k
4 votes
Accepted

Mixed strategy in extensive form games with complete and perfect information

I assume that implicit in the lemma is the condition "holding other players' strategies fixed". I'll also assume that the strategy space is finite. Given a profile of the other players' ...
Herr K.'s user avatar
  • 15.4k
4 votes

Von Neumann-Morgenstern Utility Theory Question

Utility of the expected value and the expected utility of a random value are not the same things. The usual example I give, is suppose you can enter a lottery where there is a 50% chance of winning \$...
Giskard's user avatar
  • 29.3k
4 votes
Accepted

Expected Utility

the first thing to start with is to realize how the graph works. Any point inside the graph gives you three probabilities: $Prob_1$, $Prob_2$ and $Prob_3$. Remember that while you only see the first ...
Athaeneus's user avatar
  • 798
3 votes

vNM Expected Utility Theorem Proof

Let's write \begin{align} x&=ap+(1-a)r\\ y&=aq+(1-a)r \end{align} You want to show that $x\sim y$. But \begin{equation} x\sim y\quad\Leftrightarrow\quad x\not\succ y\;\text{ and }\;y\not\...
Herr K.'s user avatar
  • 15.4k
3 votes
Accepted

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, ...
Herr K.'s user avatar
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