# Questions tagged [probability]

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

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### How to approach rigorous probability theory from an economics background?

I am attempting to read around the theory of probability theory from the ground up, coming from a background of economics I have little experience in set/measure theory, whilst I am not new to ...
24 views

### Average ability conditioning on having accepted an offer

There is a continuum of workers between 0 and 1. These have ability $\alpha\sim U[0,2]$. A firm offers them a salary $v$ and has profits $$\pi = (\rho \alpha-v) n(v)$$ where $n(v)$ is the fraction ...
31 views

### Estimating probability of Central Bank's interest rate changes

Recently, I came across this article, which offers a simple model for estimating the probabilities of interest rate cut/hike from a central bank. This is done by using market data, especially normal ...
22 views

### Risk neutral probability for each of 3 states

I need help to find the risk-neutral probability for states 1,2 and 3 I have two stocks: A and B. The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3); The ...
66 views

### Modelling involving sum of random variables: Simple CDF?

This question emerges from a project in microeconomic modeling. I have $n$ agents receiving noisy i.i.d signals $s$. In my model, a situation of interest occurs when the average signal across $n$ ...
15 views

### Arbitrage checking (one step price tree)

I have a questions on arbitrage. These questions are from my lecture notes. And I don’t understand their some points. Ex1: there is a single step market as follows here, there are two securities ...
75 views

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### Lack of historical data for calibration of probability of default

It is a known fact that default rates seem to exhibit cyclic behavior. Most probability of default models use one-year averages of default rates to calibrate the models. The one-year averages should ...
178 views

### 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 ...
71 views

### 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 ...
59 views

### 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 ...
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 ...
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 ...