Questions tagged [expected-utility]
The expected utility theory deals with the analysis of choices among risky projects with multiple possible outcomes.
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How to compute this utility function's expected value
Here is the image
The utility function U is the function of $W_1$ and X, $U(\tilde W_{1i},X_i)$,
$W_0$ is the investor's wealth at moment $0$, and $W_1$ is the wealth at
moment $1$,
$r_f$ is the risk-...
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Expected utility maximization question
If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ...
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Known approaches to identify sub-portfolios in an investors' portfolio choice
I'm looking for several days already and i haven't found a satisfying idea how to approach the following problem:
I'm interested in identifying mental accounts in the form of sub-portfoios in an ...
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Deriving the CAPM: going from utility of consumption to utility of asset returns
Some textbook presentations of the capital asset pricing model (CAPM) take returns on stocks as a primitive and proceed as if agents derive utility from asset returns. Assuming a concave utility ...
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Expected Utility
I really don't know how to interpret the graph. Can someone help me?
I thought of doing 0.6253+0.3751 to find the expected value of the lottery but where is the sure bet?
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Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions
I'm currently reading the paper with the same title as this question by Mr. Toda, I attached the link below.
https://www.sciencedirect.com/science/article/abs/pii/S0304406820301373
and I have several ...
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Existence of best and worst lotteries with finite outcome set and IIA
In the context of expected utility theory, I want to prove that if the set of outcomes is finite and an agent has a rational preference relation over the set of lotteries, and if that preference ...
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Expected revenue maximizing auction & ex-post efficiency
Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?
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Convergence of various forms of Prospect Theory?
I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience.
My problem is the following: I want to analyse the effects ...
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Every expected utility form represents a preference relation over lotteries
Suppose there are finite number of prizes or alternatives. L denotes the set of all lotteries over the prizes. Does every expected utility form defined on L represents a preference relation on ...
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Von Neumann-Morgenstern Utility Theory Question
There's a question in my ECON notes that I don't understand, any help would be greatly appreciated.
Here are the definitions used about VNM Utility Theory.
The question is posted after the definitions....
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Expected value inside a utility function
Lets say Agent 1 has a utility function that depends on the other person, i.e., $u_1(x_1-x_2)$, where $x_i$ is the choice of Agent $i$. Suppose the expected value of $x_2$ is denoted $E[x_2]$.
Can $...
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On risk aversion and validity of utility functions
Question
A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences.
The investor has a current ...
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Mixed strategy in extensive form games with complete and perfect information
I saw the lemma:
"In extensive form games with complete and perfect information, any mixed strategy
for player i will result in a lower or equal utility for player i compared to some pure ...
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Experimenting with Mean Variance Analysis
here with a question about mean-variance analysis and utility theory hope you can help me.
First point
My main objetive is to maximize the expected utility from portfolios given by $\sigma_p^2=\frac{C}...
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Is it possible to have mean-variance preferences with different states of nature? Mean-Variance and Expected utility together?
I have to maximize mean-variance preferences like this (where Pi is a profit function):
\begin{align} \label{eq:9}
\max\limits_{Q_{F}^{\{x\}}}Z_{w}= E[\pi{\{x\}}]-\frac{A}{2}Var[\pi{\{x\}}]
\nonumber\\...
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Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?
Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU?
To my knowledge, most utility functions under risk and ...
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Utility of both players in St. Petersbourg paradox - behavioural economics
Im reading a paper by Karl Menger [1] about the St. Peterbourg paradox :
In the theory of probability, the "Petersburg Game" designates the
follow- ing gamei between two persons, A and B. ...
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What is the intuition behind Expected Utility Theorem?
I am referring to the definition in Proposition 6.B.3 on Page 176 of Mas Colell. I follow the formal proof and the application of the Independence axiom at various steps (mathematical application of ...
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certainty equivalent and lotteries [closed]
suppose an agent has $u(z)=-e^{-bz}$ where $b>0$ as her Bernoulli utility function and faces two gambles:
G1: win 1000 dollars with probability $\frac{1}{2}$ and zero with probability $\frac{1}{2}$ ...
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What is the expected payoff for a bidder in a second-price auction with N uniform distributed bidders, when the auctioneer sets a reserve price?
I would like to know what bidder i's expected payoff looks like in a second-price auction with $N=\{1,2,...,n\}$ bidders, where each bidder $i\in N$ has independent and uniform distributed valuations $...
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Model the uncertain impact of a proposed policy by expected utility or other probabilistic approach
The impact of a proposed policy is often uncertain and subjected to randomness. As such, it seems natural to use probabilistic models. How to model the policy impact using the expected utility ...
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How to empirically measure the underlying utility function for a 'max EU" SWF? Stated/revealed preferences over uncertain lotteries, or?
Direct answers, as well as pointers to the best literature and textbook treatments, as well as the names of key researchers, are appreciated.
Suppose we are considering policies and transfers that ...
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How does this imply that a Pareto optimum maximizes a weighted average of utility functions?
I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me.
In the passage, Back is ...
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Von Neuman-Morgenstern utility theorem apply only to linear utility functions?
Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...
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Analyzing a Gambling Race Paradox
Suppose a number of players are given $100$ points each, and repeatedly engage in a gamble having positive expected value, with the goals of being the first player to reach $100000$ points. Solving ...
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What would be the Dual Expected Utility function for an English Auction?
So the DEU function is $$V(p)= \Sigma \,x_i\pi_i(p),$$ and since an auction only has two outcomes for a bidder, failure (with probability $p$) or success (probability $1-p$) the function becomes $$V(p)...
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What is the consensus (if any) on Peters "The ergodicity problem in economics" (2019)?
Peters (2019) made a splash criticizing the theory of expected utility on the grounds that it implicitly assumes ergodicity where this is unwarranted. He stated this applies widely in economics, to ...
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Deducing beliefs from choices when the Savage Axioms are true
We know, that given a set of possible outcomes $X$, a set of states of nature $\Omega$, and the set of all acts from $\Omega$ to $X$, if a DM has rational preferences over the acts and if the Savage ...
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Repeated betting game with positive expected value
Consider the following basic repeated betting game:
A player can enter the game with an amount of money x.
The game consists of multiple rounds.
In each round a ...
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Expected utility theory (Lottery notation)
A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences
$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$
...
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Comparing & contrasting decision problems and normal games
I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.
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Why utility rather than expected utility in Cochrane's "Asset Pricing"?
Cochrane "Asset Pricing" Chapter 1 p. 6 says
We model investors by a utility function defined over current and future values of consumption,
$$
U(c_t,c_{t+1}) = u(c_t) + \beta \mathbb{E_t}[...
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Is the expected utility the inverse of the utility function?
Can somebody explain to me if that it's true and also graphically explain it?
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The efficient frontier in mean variance criterion
The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance，Why do the optimal portfolios in the effcient frontier, is ...
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Need help with Wakker (2010) on arbitrage
In Prospect Theory (2010; Cambridge UP), Peter P. Wakker has an exercise assignment 3.3.6 without solution in the book and I'm really unsure about this one. The exercise states on pages 76-77:
...
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Calculating risk interest rate within a two period model
I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility ...
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Should the "value function" be "utility function" in prospect theory?
I have a background in mathematics rather than economics, and currently reading Choices, Values, and Frames[1]. The paper defines a "hypothetical value function" (the s-shape that is concave ...
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Fair value that a risk averse individual would pay to enter a gamble
Introduction
Assuming an individual (or corporation) with risk aversion and a von Neumann-Morgenstern utility curve and given a gamble g with E(g) > 0.
From what I researched, certainty equivalent is ...
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How is the defintion of the mean preserving spread (MPS) not too general?
The mean preserving spread is defined as follows:
Consider two lotteries g and h. Let $x_g$ und $x_h$ denote the corresponding random variables. Then h is a mean preserving spread (MPS) of g, if:
$...
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Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?
This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference ...
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Understanding Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion
I am trying to understand Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion.
I am struggling to completely understand the following:
Suppose you have initial wealth of $W$...
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Diminishing mariginal utility and risk preferences
Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it ...
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If the marginal cost is equal to 1, how does that imply marginal cost is equal to marginal benefit?
The function below is a utility function simplified after subject to an implied participation constraint.
$$
E\left(\pi_{n}\right)=e^{*}-E\left(s^{*}\right)=e^{*}-c\left(e^{*}\right)
$$ where $ \pi_n ...
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Who is the first one to equate "rational" with "complete and transitive preference"?
MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first?
vNM said ...
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Why is the risk premium always positive for risk averse individuals?
I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.
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Intertemporal choice with possibility of death
Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$...
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Why can we write any lottery as a convex combination of the degenerate lotteries?
I know that a degenerate lottery is a lottery that yields outcome $n$ with probability $1$ and I also know the definition of convex combination: given $x_{1},x_{2}, \cdots ,x_{n} \in \mathbb{R}$, a ...
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How to prove the relationship between the expected value of a lottery and its certainty equivalent?
Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent).
(Definition of $CE$: the ...
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Expected Utility and Jensen's Inequality
Consider two random variables (costs and valuations) distributed $v\backsim G(.)$ and
$c \backsim F(.)$ with pdfs $g(.)$ and $f(.)$. Let the supports of $c$ and
$v$ be $[x,y]$. Let $x<a=E(v)<b&...
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