12
votes
Would insurance plan be necessary if we had instant access to credit?
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 ...
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11
votes
Would insurance plan be necessary if we had instant access to credit?
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 ...
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7
votes
Accepted
Can the Certainty Equivalent be negative?
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 ...
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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 ...
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5
votes
Experiments contradicting the expected utility model
Picking up my comment under this answer.
One striking issue relevant to decisions not captured by expected utility is the framing effect discussed by Tversky and Kahneman (1981) and others.
In their ...
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5
votes
Accepted
Proof that independence implies monotonicity in Osborne and Rubinstein
You're right. The proof is provided for the proposition
$\alpha > \beta \implies \alpha \cdot a \ \oplus (1-\alpha) \cdot b \succ \beta \cdot a \ \oplus (1-\beta) \cdot b$
But note that proving the ...
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4
votes
Would insurance plan be necessary if we had instant access to credit?
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 ...
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4
votes
Would insurance plan be necessary if we had instant access to credit?
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 ...
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4
votes
Experiments contradicting the expected utility model
Let me mention another quite well-known one: The calibration theorem by Rabin (2000) and Rabin and Thaler (2002). The idea is that over small stakes individuals must be essentially risk-averse, but in ...
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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 ...
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4
votes
Accepted
A growth model with regime switch
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, ...
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4
votes
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Why Certainity Eqivalence in PIH only holds for quadratic utilities
Certainty equivalence in the context of the Permanent Income Hypothesis implies that $u'(E_t[c_{t+1}]) = E_t[u'(c_{t+1})]$, which only holds if marginal utility $u'(\cdot)$ is linear (by linearity of ...
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4
votes
Can we compare risks of lotteries?
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 ...
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4
votes
Comparing & contrasting decision problems and normal games
Decision under uncertainty is sometimes called a "game against chance", and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states ...
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4
votes
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Arrow-Debreu Market with Uncertainty
There are several ways to "decentralize" trades, but it is easiest to think that all trades are made before any uncertainty is revealed. Then $\hat{p}_{t}\left(s^{t}\right)$ is how much an ...
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3
votes
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Existence of 'best' and 'worst' lottery
Hint
Let $\{1,2,\dots,N\}$ be the set of outcomes. Without loss of generality, let $1\succsim 2\succsim\cdots\succsim N$. Let $\mathbf e_i$ denote the degenerate lottery that assigns probability $1$ ...
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3
votes
Accepted
Question on uncertainity
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 ...
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3
votes
What exactly is certainty equivalence in the context of DSGE models?
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, ...
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3
votes
Accepted
von-Neumann-Morgenstern v. Bernoulli Utility Function
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, ...
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3
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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 ...
- 1,380
3
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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 ...
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3
votes
Can we compare risks of lotteries?
Risk is a subjective measure. Perhaps climbing a tree is very risky for me, while you think it is a child's game and entails no risk. Intuitively this is why there are many ways to define risk, for ...
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3
votes
Uncertainty and Pareto efficient policies
Pareto efficient allocations can be found by maximizing a weighted average of the utilities of the agents. Let $\lambda$ be the Pareto weight for agent 1 and $1 - \lambda$ the weight for agent 2 (...
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3
votes
Accepted
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 ...
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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 ...
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3
votes
Volatility indexes
This question is better suited for Quantitative Finance StackExchange.
You should not rely on VIX for anything outside of the US (or not related to the S&P 500 index). The CBOE used to have a VIX ...
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3
votes
Accepted
What is the intuition behind Expected Utility Theorem?
The expected utility theorem (EUT), first and foremost, establishes a utility representation of the preference over lotteries. This is akin to establishing utility representation of preference over ...
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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....
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3
votes
Accepted
Von-Neumann vs Bernoulli Utility? Do properties of Bernoulli translate to VNM?
Terminology is not uniform; many authors call Bernoulli utility functions von Neumann - Morgenstern utility functions or just utility functions.
Expected utility is linear in lotteries and, therefore, ...
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3
votes
Accepted
Lotteries in an equilateral triangle
Consider an equilateral triangle of side length $\frac{2}{\sqrt{3}}$. If we pick any point inside the triangle and drop perpendiculars to the three sides of the triangle, then the length of these ...
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