All Questions
Tagged with expected-utility utility
47 questions
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A Measure Theory\Probability Question Regarding Model Setting of Ambiguity (Schmeidler (1984, 1989))
In David Schmeidler (1984), "Subjective Probability and Expected Utility without Additivity", "2. Axioms and Background", there is a setting:
Let $X$ be a set and let $Y$ be the ...
2
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0
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35
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Degrees of Risk aversion and Expected utility [closed]
There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
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34
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Comparing agent decision-making under risk-neutrality and risk-Aversion
I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows:
There is a technology (for example, a vaccine) which reduces the ...
- 41
1
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1
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105
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How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?
Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
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1
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93
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How special is the "expected value" operator in Von Neumann–Morgenstern utility theorem?
The Von Neumann–Morgenstern utility theorem states that
For any VNM-rational agent (i.e. satisfying axioms 1–4), there exists a function $u$ which assigns to each outcome $A$ a real number $u(A)$ ...
- 139
2
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1
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80
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Proof of the Lucas' Cost of Business Cycles
I am trying to derive the parameter used by Lucas to measure the cost of business cycles, namely:
derived in the paper "Macroeconomic Priorities".
I already searched in several papers but I ...
0
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0
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122
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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 ...
- 2,611
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34
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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 ...
- 303
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1
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539
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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....
2
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1
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154
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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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3
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1
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177
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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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0
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61
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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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1
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1
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178
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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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1
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534
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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 ...
- 121
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114
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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 ...
- 498
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1
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303
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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
$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$
...
- 171
1
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1
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249
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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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1
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314
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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?
- 11
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1
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202
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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 ...
- 33
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32
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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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1
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842
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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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1
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320
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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 ...
3
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1
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166
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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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1
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786
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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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3
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1
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133
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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:
$$...
- 131
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1
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351
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How to prove the relationship between the expected value of a lottery and its certainty equivalent?
Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent).
(Definition of $CE$: the ...
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2
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188
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Algebraic approach towards convexity
I have a function: $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
1
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189
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derive value function from utility function
We have the utility function.
$$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$
And I am trying to find the value function.
$U$ is utility function. $c_t$ is consumption at ...
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456
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Proof: Risk averse; Certainty Equivalent smaller than expected value
I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds:
The certainty equivalent, $CE(\cdot)$, is ...
6
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1
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149
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Meaning of $dF(z)$ in expected utility framework
Background: from a Microeconomics course,
$F$ is a cdf. In other words, if $F$ has a density function $f$, then
$$F(z)={\int_{-\infty}^z f(x) dx} $$
Write the Bernoulli utility function $u:...
- 213
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1
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85
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Theories that complement/contradict prospect theory?
Kahneman and Tversky's prospect theory, which they developed to contradict expected utility theory, is obviously an interesting result.
But, after their experiments has anyone tried to completement ...
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1
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29
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advanced mathematical treatement of revealed preference and utility theory?
I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel.
What would be suggestions for this? Specifically I'm interested in conditions ...
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3
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1
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113
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Construct utility function for a risk-averse agent
I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
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2
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1
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304
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Modelling Bounded Utility Functions
I'm trying to work out how to model a utility function that is bounded below some level. More precisely, given a specified limit $L$, I want to work out how to ensure that the utility of any outcome $...
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1
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175
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Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?
We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$.
Are there intuitive interpretations of the numerical values of these ...
- 837
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1
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282
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Maximal Allais paradox
The Allais paradox, is an experiment set up as follows, where you are free to chose between gambles $A$ and $B$:
(the table on wikipedia is much more readable if you prefer)
Experiment 1
...
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3
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1
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140
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Additive multiattribute nonlinear utility functions
I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form:
$u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \...
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2
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431
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Why should the statistical value of life exist?
In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts. So economists have ...
1
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2
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765
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Transforming expected utility functions
I am using the following theorem:
To better understand how I can transform expected utility functions.
An example with which to work:
I want to show that the preferences represented here satisfy ...
- 2,911
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2
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910
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How to have same utility function for two persons?
I have a question regarding utility functions:
Utility can be defined as follows:
$U=1+e^{\frac{x}{RT}}$
U:Utility
x: What we want to find the utility for (Certain equivalent)
RT: Risk tolerance
...
- 101
3
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66
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Utility theory or decision theory based on partial semiorders?
Roubens, Vincke & Pirlot have summarized and extended representation theorems for partial semiorders in the 80s and 90s. See e.g. Roubens, M. & Vincke, P.: Preference Modelling. Springer, 1985....
1
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1
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187
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Conceptual explanation/prediction of utility function. Extraction of utility function from Big Data
It seems to me, that utility function usually is just a set of facts. Is there a framework or model for utility function that can explain or predict utility function. I. e. if user has value for item ...
- 435
2
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1
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277
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How do I find out which form of utility function is being used?
Can someone tell my how i can figure out which type of utility function the following maximization problem has. It is for an overlapping generations model.
$$\underset{x'}{\max} x'\big(E_t (P_{t+1}+...
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3
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2k
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Question about the Ellsberg Paradox in Expected Utility Theory
The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
11
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3
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1k
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Does risk aversion cause diminishing marginal utility, or vice versa?
Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
0
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1
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524
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Question about constant relative risk aversion
The question:
Consider a person with constant relative risk aversion $p$.
(a) Suppose the person has wealth of $100,000$ and faces a gamble in which he wins or loses $x$ with equal probabilities. ...
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14
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3
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223
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Current knowledge about the empirics of consumer theory
I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.).
Can anyone ...
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