12

As Dave Harris' points out in his comment, I assume that your question deals with events that do not compromise the individual's ability to work, which would prevent her from taking on debt. Let's take the example of a fire which happens with probability $\pi \in [0,1]$. The damage of a fire equals $D$ dollars, i.e. it costs $D$ dollars to repair the house. ...


11

I think the best way to answer your question is with a simple example showing why insurance is so prevalent in the economy. Hopefully, it should then be clear that it can still make sense to purchase insurance even if you can take out a loan to "cover the recent loss/accident". Suppose that there is a 1% chance of a £10,000 loss occurring. For a concrete ...


10

this paper http://else.econ.ucl.ac.uk/papers/uploaded/243.pdf (Choi 2007) has a nice state of the art experiment that deals with rationality and expected utility is a special case of it. In general only 17% of consumers are compatible with rationality ergo the remaining part cannot be expected utility maximizers. Quah has a nice paper on the revealed ...


8

To understand why $\alpha$ must be constrained in $(0,1)$, one has to contemplate the meaning of the expression $$\alpha L$$ when $L$ is a "lottery". How is a lottery denoted mathematically? Authors do not agree on that: for example, the way Jahle and Reny define a lottery (a "gamble" in their terminology), a lottery can be written as a vector whose ...


7

Adding to the list of paradoxes, consider Machina's paradox. It is described in Mas-Colell, Whinston and Green's Microeconomic Theory. A person prefers a trip to Paris to watching a television program about Paris to nothing. Gamble 1: Win a trip to Paris 99% of the time, the television program 1% of the time. Gamble 2: Win a trip to Paris 99% of the time, ...


7

If you start out with €0, then the certainty equivalent of losing €2.5 with probability 1 is -€2.5. Your exercise basically asks you to calculate what difference winning the lottery with a small probability makes. Given this utility function, not much.


6

No Time To Argue Most importantly, there cannot be an "18 months period of notice". Tt has to be decided suddenly and there cannot be any period in which individuals could respond to the new plan by withdrawing their money and moving cash from one of the member countries to any of the others. New Currencies Each country has to have its own currency. These ...


6

No, I would not say that this resolves the Machina paradox, because it is exactly the same as the Machina paradox: the paradox does indeed require from you to look at the three possible outcomes. The M-C/W/G book discuss only the $B$ and $C$ outcomes because it is there where the paradox focuses on whether a violation of the axiom of independence may happen. ...


5

This is perhaps a good opportunity to point out that the "certainty equivalence" concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in macroeconomics. Microeconomics/choice under uncertainty The Certainty Equivalent of a lottery/gamble, is the amount of wealth which, if given with certainty, ...


4

Your notation is a bit misleading: it would be better to write $\mathbb{E}u(p)$ or $U(p)$ for the expected-utility associated with $p$ instead of $u(p)$, and $u(\mathbb{E}p)$ for the utility of the expected value of $p$. Formally $u$ is defined on $X$ and not on $\Delta(X)$. Regarding your proof, it seems to me that: $(i)$ you don't explain how to find $s$; ...


4

Insurance: pooled risk. Loan: borrowing against future income. With insurance, you may face higher premiums if you make a claim. But you won't pay anything against the claim itself. With a loan, you are responsible for paying the claim. You pay some of it with past income (savings) and some with future income (borrowing). But in the end you pay ...


4

Not covered by the other answers: You have an accident in your car and it ploughs into a bus-stop severely injuring and permanently incapacitating several people. Not having insurance, you are presented with a demand for £10,000,000(*) to cover ongoing medical costs. How long do you think it would take to pay off this loan? (*) Figure plucked from air, but ...


4

I think you are correct that this solves the Machina Paradox but I am not sure I would associate your reformulation of the model with the idea of state-dependent utility. State-dependent utility is more than a mere extension or modification of the set of outcomes of the expected utility model. To make sense of state dependent utility, you need to have a ...


4

This topic has been studied widely in the theory of repeated games. See for example: Robert J. Aumann, Sylvain Sorin: Cooperation and bounded recall, Games and Economic Behavior, Vol. 1, No. 1. (March 1989)


4

Maybe not what you are looking for, but a related concept is regret. Orphanides and Zervos (1995) is a classic paper on rational regret in a health economics concept http://www.jstor.org/discover/10.2307/2138580?uid=3739840&uid=2&uid=4&uid=3739256&sid=21106216442271 There's also plenty of irrational regret papers, mostly just boiling down ...


4

People have argued that if the rich countries (sometimes just Germany) left the Euro the resulting dislocations would be much smaller: German departure would be less disruptive than Grexit for three reasons. First , a Greek devaluation would trigger capital flight from the next weakest country – Spain, then Italy and France. Germany would not ...


4

Knight's 1921 essay was not written in formal mathematics (and trying to formulate a direct translation into modern mathematics may be quite problematic). Since Knight's time, a formal decision theory literature has developed which makes distinctions that are at least reminiscent of Knight's. Lars P. Hansen (2012), writes "Motivated by the insights of ...


4

Continuing on the comments exchange, the conclusion that the overall effect is to change the discount factor, is similar to the one reached in the original Overlapping Generations Model of Blanchard, where individuals are faced with a "probability of death" (surely a "catastrophic event" I believe). See the Blanchard & Fischer book "Lectures in ...


4

You might be looking for the concept of stochastic dominance: Roughly speaking, first order stochastic dominance of distribution A over distribution B, means that for every possible outcome gamble A pays out weakly more and in at least one state it pays out strictly more. Roughly speaking, second order stochastic dominance means that distribution A has the ...


3

Following @Pburg answer and the subsequent discussion in the comments, I wanted to post an alternative Machina Paradox I thought of. Although it might be less pervasive in real life, it seems stronger to me in the sense that it does not rely on some kind of complementarity between the "different" components of each outcome. Consider the following alternative ...


3

Just to add to the discussion of momentum, there is a new paper by Novy Marx on this topic: http://rnm.simon.rochester.edu/research/FMFM.pdf. In the paper, he argues that the price momentum that we observe is actually earning momentum. So this pushes the puzzle to a more fundamental variable rather than just pure price. However, earning momentum itself is ...


3

The Jegadeesh and Titman (1993) paper is usually considered Original Source, though I'm sure you could find something earlier that looks similar if you looked hard enough. I don't think there is a satisfactory explanation. Momentum is not correlated with macroeconomic variables, it does not seem to reflect persistent exposure to other (known) sources of ...


3

Too long, didn't read: the market does not care. Colombia's Pension Reform: Fiscal and Macroeconomic Effects, by Klaus Schmidt-Hebbel, states black on white (p 22) that issuing explicit domestic debt for paying off implicit government debt does not have first-round macroeconomic and financial effects on the condition that the financial markets see ...


3

There are many ideas to look into and some research: IDEAS Elections are presumably a time where the future becomes uncertain in the sense that there is a likelihood the new leader will change the course of a nation. From that point of view its about increased uncertainty. Elections are often about corruption. The current political party will use ...


3

You are right, but to make sure that the odds are really exogenous ("objective") you need to make sure that the subjective uncertainty has no bite here. In other words, you need to assume that the objective lottery played after the horse race is independent of the result of the horse race (in Anscombe-Aumann's terminology). Let's assume that $Z$ is finite, ...


3

Bernoulli utility represents preference over monetary outcomes. In a way, this is no different from the typical utility functions defined over consumption bundles. vNM utility, in contrast, represents preference over lotteries of monetary outcomes. Thus, the argument of vNM utility is an object related to, but categorically distinct from, the object that ...


3

I finally found a reference that defines the terms risk and uncertainty the way I do. Sven Ove Hansson "Decision Theory: A Brief Introduction" (1994) writes on p. 27-28: In one of the most influential textbooks in decision theory, the terms are defined as follows: "We shall say that we are in the realm of decision making under: (a) Certainty if ...


3

At the risk of being a bit repetitive from my earlier comments, I believe there are a few notable caveats and assumptions made in my answer. Wherever possible, I’ll try to highlight the assumptions made, and how they impact my opinions. That said, any clarification you can provide regarding what exactly your project’s scope and goals are, the more I can ...


3

Intuitively, it means that the model has such characteristics that "the best we can say" about remaining uncertainty, is that it will be zero. From general experience, we know that it won't be zero, but the information we possess does not permit us to say anything else than that it will be zero. The even deeper assumption here is that the information and ...


3

We are given that $u$ is increasing and concave, and $u(0) = 0$. This implies that $\dfrac{u(t)}{t}$ is decreasing in $t$, and also, $\dfrac{u(t)}{t} > u'(t)$ for all $t$. Nicole's maximization problem : \begin{eqnarray*} \max_{x} \ q(x)(w-t(x))\end{eqnarray*} FOC : $q'(x)(w-t(x)) = q(x)t'(x)$ Suppose $x_N$ solves Nicole's problem. Therefore, it ...


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