# Questions tagged [probability]

A branch of statistics that studies the likelihood of uncertain events occurring.

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### Pricing a European call option while absence of arbitrage is violated

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
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### To bet or not to bet

Your utility from having $x$ dolars is $u(x)$. There is a gamble in which the winnings in dollars are a random variable, $Y$. It is known that $E[u(Y)]>E[u(1)]$, so you prefer to bet than to get ...
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### Proof that the diff-in-diff (wrt sample size) of the expectation of a first-order statistic is positive (Stigler 1961)

I'm trying to prove a claim made in Stigler (1961), "The Economics of Information." This claim has to do with showing that the marginal benefit of making an additional search (e.g., searching an ...
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### Urn balls and probabilities

Think of the following balls as individuals of populations. Say I have $U$ urns, and some balls. Both numbers are really large. So large, that authors like Blanchard and Diamond have approximated ...
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### Something Terrible is Happening - But When Is it Likely to have Happened?

We live in continuous time $t$ and something terrible is happening at a poisson rate of $r(t)$. How can I compute the length $T$ such that with a probability of $P$ (for example, 0.99), at least one ...
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### When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?

Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc. When $f$ is ...
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### Is there a name for this type of problem?

I am having trouble formulating the concept I am thinking about. It has to do with looking at observed behavior of the sales of a particular product during each hour of the day, and trying to adjust ...
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### Normalizing comparisons of corporations and countries

When publicly-traded corporations reach record valuations, articles in the media often compare such valuations to the GDPs of countries throughout the world, typically in the form "Company X's ...
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### Example of the change of measure proposed in Hansen (2012)

In this question, I'm continuing to explore the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies" (2012). I'm trying to compute an ...