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8 votes
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Second order stochastic dominance

The answer to 2. is no. One way to see this is from MWG's Property 6.D.2: $F$ SOSD $G$ if and only if \begin{equation} \int_0^xF(t)\mathrm dt \le \int_0^xG(t)\mathrm dt \quad\text{for all }x. \end{...
Herr K.'s user avatar
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7 votes

Why is everyone suggested to specialize their education?

Note: I did not vote down on this question, and it is not clear why anyone would do so. Why is so common to suggest university students to specialize in order to get a better paid job? Because ...
Iñaki Viggers's user avatar
7 votes

Second order stochastic dominance

The answer to 1. Your conjecture is correct. Consider lotteries $A,B$ where $A$ guarantues a payoff of 1 while $B$ yields 0 or 4, each with 50% probability. $B$ does not SOSD $A$, as you can easily ...
Giskard's user avatar
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6 votes

Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Many people accept the axiomatizations of expected utility as normatively appealing, especially in contexts of pure risk. For people with this view, rational decision-makers should behave in ...
Michael Greinecker's user avatar
5 votes
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Why is the risk premium always positive for risk averse individuals?

Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(...
lunar_props's user avatar
4 votes

References for particular definitions of risk and uncertainty

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 ...
Matthew Gunn's user avatar
4 votes

What is the average economic value of a human life?

As a graduate in health economics, I'd use the QALY threshold to answer this question. A QALY is a quality adjusted life year i.e., a year in perfect health-related quality of life, two years with 50% ...
tomerr's user avatar
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4 votes

How is an interest swap collateralized

I can clarify a few points that @Brian Romanchuk raised. Nowadays newly transacted US$ interest Rate swaps must be cleared at a clearing house, unless the client claims an exemption (for example, ...
dm63's user avatar
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4 votes
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Is Epstein-Zin utility a generalization of dynamic expected utility (DEU)?

Epstein-Zin (EZ) preferences are a generalisation of dynamic CRRA preferences. In standard CRRA preferences, i.e. $$ U(c_0,\dots) = \mathbb{E} \left[ \sum_t \beta^t \frac{c_t^{1 - \rho}}{1 - \rho} \...
Walrasian Auctioneer's user avatar
3 votes
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Construct utility function for a risk-averse agent

If $-|x-a|$ represents the monetary payoff associated with the policy choice $a$, then $u(a) =-\left(|x-a|^\gamma\right)$ is risk averse for $\gamma > 1$, and risk loving for $0<\gamma < 1$.
Amit's user avatar
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3 votes

References for particular definitions of risk and uncertainty

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 ...
AndrewC's user avatar
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3 votes

References for particular definitions of risk and uncertainty

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 ...
Richard Hardy's user avatar
3 votes

How to estimate market risk using only publicly available data?

This paper on Fluctuations in Uncertainty may be helpful and relevant. The volatility of the stock market or GDP is often used as a measure of uncertainty because when a data ...
emeryville's user avatar
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3 votes

Why does Mascolell define second-order stochastic dominance as such?

The motivation is I believe clearly stated in p. 197 beginning of the section, where they write that they want to use Second-order stochastic dominance to reflect comparisons related to "riskiness/...
Alecos Papadopoulos's user avatar
3 votes

Negative expected value; risk neutral choice

There are three type of individuals : risk averse, risk neutral and risk loving. Individuals evaluate risky prospects such as to maximize the expected level of their utility. So, an agent is risk ...
ARandomUser's user avatar
3 votes
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Can we model risk with only probability?

I don't think it even makes sense to talk about risk without specifying the payoffs. Take your two examplary gambles and suppose that $a=b=c=d=e=0$. In that case, there is no risk involved at all. It ...
Bayesian's user avatar
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3 votes
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Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

$p\circ x\oplus(1-p)\circ y$ is a lottery that gives you the prize $x$ with probability $p$ and the price $y$ with probability $(1-p)$. Unless $x,y$ can be identified with numbers, such as amounts of ...
Michael Greinecker's user avatar
3 votes

Choice under uncertainty

Let $c$ be the cost per unit of insurance, so the premium is equal to $cn$. Then the agent maximises: $$ p(u(w - L - cn + n) + (1-p)u(w - cn). $$ The first order condition with respect to $n$ is given ...
tdm's user avatar
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3 votes
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Bond Price expression

If $ \delta > 0 $ is very small, then the interest incurred during the small subperiod $[t, t + \delta]$ can be approximated using the simple interest formula. More specifically, the interest ...
user141240's user avatar
3 votes

Negative certainty equivalent

I mispoke in the comments, this certainty equivalent should indeed not be negative. The certainty equivalent in your example is $w_0+c$, this certain payoff's utility is equivalent with the lottery's....
Giskard's user avatar
  • 29.4k
3 votes
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Why does Central Bank Digital Currency affect commercial banks' retail deposits?

Because they are substitutes and they compete with each other. The more substitutes there are for a product the lower the market power of a producer of that product. Today if you want to buy anything ...
csilvia's user avatar
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3 votes

What was the original paper that showed that estimates of risk aversion from micro and macro are inconsistent?

The literature was initially quite pessimistic about the possibility to consistently estimate risk-aversion parameters consistently (and more generally all models' parameters), as highlighted by ...
Bertrand's user avatar
  • 3,371
3 votes
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What was the original paper that showed that estimates of risk aversion from micro and macro are inconsistent?

In an extremely influential paper, Mehra and Prescott (the reference is below) showed that in order to explain the premium of stocks over treasury bonds in a parametric general equilibrium model, one ...
Michael Greinecker's user avatar
2 votes
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Swaps and systemic risk

A standard ("vanilla") interest rate swap is a contract in which one party pays a fixed rate of interest, and the other pays a floating rate (typically LiBOR, but it depends upon the market convention ...
Brian Romanchuk's user avatar
2 votes

Are risk-costs a form of external costs?

In the particular case of nuclear power plants, yes, the risk cost can be considered as a negative externality. That's because nuclear power plant operators are explicitly limited by law in their ...
410 gone's user avatar
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2 votes
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Consequentialist View of Risk

This assumption is usually considered as reasonable from a normative perspective. For instance, consider the following situations: in situation A, you face an urn with 5 blue balls and 5 red balls. A ...
Oliv's user avatar
  • 3,252
2 votes

VaR and rating for commercial banks

I restrict myself to credit rating for Banks only. There are different solutions, in bold are my preferred one. To have just an idea about single banks register a free user account to rating ...
FabIO's user avatar
  • 51

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