Questions tagged [uncertainty]

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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 ...
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1answer
32 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 ...
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1answer
35 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, ...
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Brownian motion - expected value

Could somebody explain why the expected value of Brownian motion is zero? Why is it important in economics? Thanks!
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0answers
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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 ...
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1answer
71 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
36 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 ...
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1answer
87 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 ...
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1answer
249 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
53 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
107 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 ...
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1answer
58 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 ...
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1answer
390 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 ...
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1answer
50 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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5answers
542 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
136 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, ...
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1answer
3k 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 ...
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1answer
239 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
71 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
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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 ...
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1answer
162 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(...
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1answer
225 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 ...
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2answers
403 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 $P'$ $\implies$ $aP + (1-a)P''$ ...
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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 ...
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1answer
199 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 ...
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2answers
231 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 ...
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1answer
248 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 ...
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1answer
393 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 ...
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1answer
421 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 ...
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0answers
319 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 ...
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2answers
251 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 ...
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1answer
57 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 ...
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1answer
81 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-...
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2answers
174 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 ...
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2answers
657 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 ...
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1answer
649 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 ...
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2answers
586 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-...
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6answers
511 views

Experiments contradicting the expected utility model

This is a question I asked on the cognitive science beta, but which never got any answer. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?),...