Questions tagged [uncertainty]
The uncertainty tag has no usage guidance.
44
questions
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0answers
22 views
Certainty equivalent and risk premium
I'd like some guidance on the below practice question on uncertainty in consumer theory. I think I am confused on the certainty equivalent & risk premium or I'm not understanding the question. ...
3
votes
1answer
68 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:
$$...
-1
votes
1answer
49 views
How to prove the relationship between the expected value of a lottery and its certainty equivalent?
Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent).
(Definition of $CE$: the ...
0
votes
0answers
23 views
Incomplete markets vs complete markets in permanent income model
Consider the standard permanent income model:
$$\max_{\{c_t\}_{t=0}^\infty, \{b_{t+1}\}_{t=0}^\infty} \mathbb{E}_0 \left\{ \sum_{t=0}^\infty \beta^t u(c_t)\right\}$$ s.t. $$c_t + b_t = R^{-1} b_{t+1} +...
2
votes
0answers
28 views
First order condition of the sequence problem
Consider the standard permanent income model:
$$\max_{\{c_t\}_{t=0}^\infty, \{b_{t+1}\}_{t=0}^\infty} \mathbb{E}_0 \left\{ \sum_{t=0}^\infty \beta^t u(c_t)\right\}$$ s.t. $$c_t + b_t = R^{-1} b_{t+1} +...
0
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0answers
18 views
Kreps Porteus Certainty Equivalent Intuition
In Epstein-Zin recursive preferences, the Kreps-Porteus certainty equivalent is defined by
\begin{equation}
\mathcal{R}_t(V_{t+1}) = (\mathbb{E}_t V_{t+1}^{1 - \gamma})^{1 /(1 - \gamma)}.
\end{...
0
votes
1answer
15 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
votes
1answer
43 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
votes
1answer
42 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, ...
0
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0answers
22 views
Brownian motion - expected value
Could somebody explain why the expected value of Brownian motion is zero?
Why is it important in economics?
Thanks!
1
vote
0answers
20 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
134 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?
1
vote
0answers
58 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
98 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 ...
3
votes
1answer
271 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. ...
-1
votes
1answer
54 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 ...
0
votes
2answers
144 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
60 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 ...
4
votes
1answer
509 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? What ...
5
votes
1answer
54 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 ...
8
votes
5answers
615 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" ...
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2answers
145 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
votes
1answer
4k 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
votes
1answer
280 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 ...
1
vote
1answer
74 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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votes
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
175 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(...
3
votes
1answer
239 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
votes
2answers
428 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 $P'$ $\implies$ $aP + (1-a)P''$ ...
4
votes
1answer
99 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
217 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
260 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
votes
1answer
266 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
431 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 ...
5
votes
1answer
443 views
Independence axiom of lottery when $\alpha \ge 1$
When studying preference over lotteries we learned the independence axiom which goes like this:
The preference relation $\succsim$ on the space of simple lotteries $\mathscr{L}$ satisfies the ...
2
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0answers
343 views
Probability of states of nature
I've been given the following question and would really appreciate any help on part a. I've looked over all of my resources for this course and we have always been given the probability of the ...
12
votes
2answers
258 views
Economics of forgetting
I'm interested to know economic justifications of forgetting in various fields.
On example is Green and Porter(1984). To sustain a Cartel, Cartel members have incentive to forget deviations in a ...
4
votes
1answer
58 views
What's the status on uncertainty shocks?
Bloom (2009) analyzes the impact of uncertainty shocks, and Bloom et al (2014) propose a business cycle model based on these shocks.
It seems to be a young field, but is there any consensus on ...
4
votes
1answer
82 views
Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
I'm trying to understand the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies." In a part in the paper, Hansen introduces a long-...
12
votes
2answers
177 views
How could the Euro zone be broken up in an ordered way?
Let’s assume that the members of Euro zone all agreed that it would end in 18 months time with each country getting its own currency.
What process could be put in place to allow this to happen ...
8
votes
2answers
695 views
How is momentum justified as a common risk factor?
Momentum as a common risk factor?
This question is partly a follow-up to another question found here. In this other question it was noted in momentum is difficult to explain as a common risk factor ...
6
votes
1answer
657 views
What is the advantage and disadvantage of fiscal illusion policy in terms for the financial market?
What is the advantage and disadvantage of fiscal illusion policy for the financial market?
Fiscal illusion suggests that when government revenues are not completely transparent or are not fully ...
10
votes
2answers
619 views
Can the Machina Paradox be solved by expanding the choice set?
In another question, the Machina paradox is mentioned as a possible counterexample to the expected utility model:
Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-...
17
votes
6answers
562 views
Experiments contradicting the expected utility model
This is a question I asked on the cognitive science beta which never got any answer there. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?)...
