Questions tagged [uncertainty]
The uncertainty tag has no usage guidance.
60
questions
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Risk Aversion under Worst Case Utility Representation
The preference relations (≿A and ≿B) over lotteries is defined as:
p ≿ q iff min{v(z) : p(z) > 0} ≥ min{v(z) : q(z) > 0}
Under what conditions can you say that ≿A is more risk averse than ≿B?
0
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1answer
53 views
Negative certainty equivalent
Let us consider an agent of initial wealth $w_0$ whose utility function is $u(x)=\sqrt{x}$. This individual faces a risk of loss $Z$ which occurs with probability $p$.
It is assumed that $w_0=60000$, $...
4
votes
2answers
163 views
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 ...
0
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0answers
11 views
Volatility indexes
I want to use a volatility index as a measure of economic policy uncertainty. The index that I want to use is CBOE Volatility Index: VIX, but I don't know if I only can use this for US or if I can use ...
2
votes
1answer
44 views
Drawing a Probability simplex
There are 3 possible payoffs - \$4, \$9 and \$36. The utility function for these payoffs is $\sqrt x $.
I have to find all the lotteries preferable over getting $9 with probability 1 in a probability ...
1
vote
1answer
40 views
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 $\frac{1}{2}$ ...
0
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0answers
32 views
comparing two lotteries
Suppose the prize space (in dollars) is $\mathbb{Z}$ = {1, 2, 3, 4, 5, 6, 7, 8} and consider choices by an agent
whose preferences (over lotteries) satisfy the von Neumann-Morgenstern axioms.
A risk ...
1
vote
1answer
112 views
Choice under uncertainty
I am practising past micro economics questions from the internet and I am not sure how to proceed with this question:
Imagine a situation where a risk averse agent has positive wealth(w) and may face ...
2
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0answers
37 views
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 ...
0
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1answer
55 views
Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$
I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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0answers
37 views
Pure Nash equilibrium in bidding game?
According to the answer key for a problem set, there is no pure strategy Nash equilibrium in the following problem. Yet I can't see why not. Could it be an error in the answer key? Here's the problem:
...
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1answer
50 views
How to Represent as a Payoff Matrix
I'm trying to represent the following as a pay-off matrix.
I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
1
vote
1answer
227 views
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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0answers
59 views
Choice under Uncertainty: Relation between the certainty equivalent and the coefficient of relative risk aversion
That's my question!
Propositon 6.C.4 (MWG (1995)): The following conditions for a Bernoulli utility function $u(\cdot)$ on amounts of money are equivalent:
(i) $r_R(x,u)$ is decreasing in $x$.
(iii) ...
2
votes
1answer
61 views
Uncertainty and Pareto efficient policies
There are two economic agents $i\in \{1,2\}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $x\in R$ and $b_{is}\in R$ is bliss point of $i$ in state $s\in\{1,2\}$. Assume $b_{1s}\lt b_{2s}$...
3
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0answers
40 views
Epstein zin and resolution of uncertainty
I'm reading Simon Gilchrist's notes here. I understood everything until and including page 14, where it reads
$$\frac{W_h^{1-\rho} + W_l^{1-\rho}}{2} \geq \frac{c_h^{1-\rho} + c_l^{1-\rho}}{2} $$
and ...
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0answers
45 views
Proof of certainty equivalence
The questions say two lotteries are denoted L1 = (0.3,0.7,0.0) and L2= (0.9,0.0,0.1) and denote c(L1) and c(L2) the certainty equivalents of those two lotteries.
Then prove L1 ≻ L2 if and only if c(L1)...
2
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1answer
518 views
Can the Certainty Equivalent be negative?
I am questioning if the CE of a lottery can be negative? For me it doesn't make much sense by definition.
I encountered this problem on the following exercise:
Imagine a case where we have a lottery(...
4
votes
1answer
53 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
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0answers
38 views
Term for risk AND ambiguity
This question is related to References for particular definitions of risk and uncertainty, which offers an excellent description of risk and uncertainty.
Just as a recap: Knight (1921) described risk ...
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3answers
321 views
Can we compare risks of lotteries?
I understand the concepts of risk-aversion, risk neutrality and risk-attraction. I wonder if it possible to compare risks between two lotteries without giving the utility function. For instance, Let ...
3
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1answer
100 views
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:
$$...
-1
votes
1answer
186 views
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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1answer
20 views
Existence of optimal strategy in a choice problem with uncertainty and information structure
Consider a decision maker choosing an action, $y$, from the finiteset $\mathcal{Y}$, possibly without having complete information about the state of the world.
More precisely, let $V$ be a ...
0
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1answer
47 views
Robust predictions in single-agent decision problem with uncertainty
I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ...
0
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1answer
49 views
Optimal strategy in a single-agent choice problem under uncertainty
Consider the following single-agent choice problem under uncertainty.
Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{v})$. First, ...
2
votes
0answers
38 views
Dominated lotteries in CPE
I have been looking into expectation-based loss aversion following Kőszegi-Rabin (2005, 2007). In particular, I find their choice-acclimating personal equilibrium (CPE) interesting, but it has a ...
2
votes
1answer
344 views
Existence of 'best' and 'worst' lottery
How can 'the best and worst lotteries exist when the set of outcome is finite and the rational preference relation satisfies independence axiom' be proven?
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0answers
124 views
Archimedean but not mixture continuous
In the context of preferences on a set of lotteries on a finite set $X$, what is an example of a preference that is independent, Archimedean but not mixture continuous?
I know the mixture continuous ...
3
votes
1answer
141 views
Why Certainity Eqivalence in PIH only holds for quadratic utilities
In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was ...
2
votes
1answer
321 views
Question on uncertainity
Please imagine that Nicole is uncertain of her future wealth. Her wealth in the bad state of the world is zero. Her wealth in the good state is $w>0$. Each state is initially equally likely. ...
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1answer
60 views
Indiference between two lotteries
Suppose that a binary relation satisfies only:
Independence axiom: $L≿L′⟺α\circ L+(1−α)\circ L′′≿α\circ L′+(1−α) \circ L′′$
Reduction to simple lotteries: For all $g$, $g~g'$, $g'$ is the simple ...
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2answers
311 views
Uncertainty in an unfair gamble
If a risk averse person is given the option of a certain amount of 2000 or playing a lottery game giving him 10000 with 25% probability, and 500 with 75%, then what would he do ?.
The bet here is not ...
3
votes
1answer
77 views
Profit maximization under uncertainity
I have a seller say S and I have a buyer say B. Buyer’s willing to pay is equal to x which is private information. But Seller believe that it falls in the range [0,x1]. Seller’s belief distribution is ...
6
votes
1answer
1k views
What exactly is certainty equivalence in the context of DSGE models?
I keep reading about certainty equivalence in the context of DSGE models.
I understand that it has something to do with "Getting rid of the expectation operator", but I'm not entirely sure? ...
5
votes
1answer
58 views
A growth model with regime switch
I have a very general question. I am reading this paper :
http://www.webmeets.com/files/papers/eaere/2015/177/Discounting-HelsinkiBlind.pdf
There is a catastrophic event probability and after the ...
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votes
5answers
938 views
References for particular definitions of risk and uncertainty
I have some doubts about risk vs. uncertainty. I have read the thread "What is the difference between risk, uncertainty and ambiguity" and have skimmed through Knight's "Risk, Uncertainty, and Profit" ...
0
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2answers
194 views
Help with a choice under uncertainty exercise [closed]
Let $u$ and $v$ be utility functions (not necessarily VNM) representing $\succsim$ on $\mathcal{G}$. Show that $v$ is a positive affine transformation of $u$ if and only if for all gambles $g^1, g^2, ...
3
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1answer
7k views
von-Neumann-Morgenstern v. Bernoulli Utility Function
A great deal of time is spent distinguishing the big $U$ (von-Neumann-Morgenstern)v. small $u$ (Bernoulli Utility Function). The v.NM function maps from the space of lotteries to real number as it ...
2
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1answer
380 views
Inc Linear Transformation of Bernoulli Utility
According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation.
What is the significance of this proposition?
The part I ...
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1answer
75 views
Consequentialist View of Risk
In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker.
From philosophical view, ...
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8answers
3k views
Would insurance plan be necessary if we had instant access to credit?
Assuming one could instantly have access to an loan to cover his recent loss/accident at an affordable interest, would it make sense to pay premium for an insurance plan?
I was thinking that it would ...
0
votes
1answer
188 views
Is car accident/theft a fair bet? [closed]
A person with a current wealth of 100,000 who faces the prospect of a 25% chance of losing his or her 20,000 automobile through theft during the next year. Since there is no upside to this event and E(...
4
votes
1answer
292 views
Microeconomics - Expected Utility Theory - Piecewise utility index, certainty equivalence, etc.
I am solving old problems from various qualifiers from different universities to prepare myself for an upcoming test. I came across this and wanted to ask if anyone can confirm my answers?
My ...
4
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2answers
499 views
Does the Independence Axiom Require Statistical Independence?
First: Given this definition of the Independence Axiom,
If for all $P$, $P'$, $P''$ in the set of lotteries over outcome space $X$, when:
$P$ preferred to $P'$ $\implies$ $aP + (1-a)P''$ preferred to ...
4
votes
1answer
105 views
What sort of impact would one expect on investment as a result of an approaching election?
I am looking to observe and possibly quantify private investment during election periods.
I am interested in any studies, particularly empirical, which discuss the impacts elections can have on the ...
2
votes
1answer
299 views
Constraints on a symmetric pareto allocation under uncertainty
I've been trying to figure out how the author came up with the constraints for this liquidity model in a textbook I'm reading.
details: http://imgur.com/TpVjg4w
$U = \pi_1u(C_1) + \pi_2u(C_2)$ where ...
8
votes
2answers
436 views
Will high computing power substitute the certainty-equivalence assumption?
Bloom in a recent JEP paper considers that "the increase in computing power has made it possible to include uncertainty shocks directly in a wide range of models, allowing economists to abandon ...
2
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1answer
355 views
Decision Theory Question: Existence and uniqueness of the certainty equivalent of p
Let $X = (x_*,x^*)$ be an interval in the real line and denote by $\Delta(X)$ the set of simple probability distributions on $X$. Consider a preference relation $\succcurlyeq$ on $\Delta(X)$ that ...
7
votes
1answer
544 views
Anscombe-Aumann Acts and Lotteries
Notation: Throughout I will let $\Delta X$ denote the set of probability distributions over the set $X$.
I have been studying expected utility theory, and especially Savage Acts and Anscombe-Aumann ...
