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3 votes

Decision theory: elicitation method

If you receive $C3$, you get lottery $C_1$ with probability $p$ and $0$ with probability $(1-p)$. $C_1$ is the lottery that gives $x$ with probability $p$ and $0$ with probability $(1-p)$. So in total,...
tdm's user avatar
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3 votes

Minimal assumption for a “certainty equivalence” exists

Here is an example that shows that certainty equivalents need not exist: Let $f:\mathbb{R}\to (0,1)$ be an increasing bijection. Let $0<\alpha< f(1)-f(0)$ Define $u:\mathbb{R}^\mathbb{N}\to\...
Michael Greinecker's user avatar
3 votes

Minimal assumption for a “certainty equivalence” exists

I take it that $u: \mathbb{R} \to \mathbb{R}$ and not $u: \mathbb{R}^N \to \mathbb{R}$ (as in the question). Otherwise $u(c)$ for $c \in \mathbb{R}$ does not make sense. tldr: if $u$ is continuous, a ...
tdm's user avatar
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1 vote

Value of information for risk neutral agent?

Assume that the forecaster tells Maria it is going to rain. Then she will go for project $A$ (rather than $B$) giving her a gain of 400. If the forecaster tells her it is going to snow, then again it ...
tdm's user avatar
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1 vote
Accepted

How do you prove NO difference in Expected Value, between gambling (probable $−$ EV) vs. investing (probable $+$ EV)?

In both cases, you are buying a lottery, which gives certain amounts of money with certain probabilities. Assume you have a gamble that gives 50 euro with probability 0.5 and 150 euro with probability ...
tdm's user avatar
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1 vote

Archimedean but not mixture continuous

Let $\succeq$ be a complete and transitive binary relation on the set of all lotteries on finite sets of prizes. Then $\succeq$ is mixture continuous if and only if it satisfies the Archimedean axiom ...
Paul H.Y. Cheung's user avatar

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