Questions tagged [probability]
A branch of statistics that studies the likelihood of uncertain events occurring.
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How to interpret the proof that information cascades will form?
I am reading the 1992 paper of Bikchandani, Hirshleifer and Welch on information cascades. They claim and prove that, given an environment of sequential decision making, an information cascade will ...
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Model the uncertain impact of a proposed policy by expected utility or other probabilistic approach
The impact of a proposed policy is often uncertain and subjected to randomness. As such, it seems natural to use probabilistic models. How to model the policy impact using the expected utility ...
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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 ...
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Mean Field/Differential Game and Measurability
Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
user11305
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Job-finding rate in an urn-ball model with types
Setup Say you have two types of workers, high and low. The share of low-types among the unemployed population is $P$. I want to find the job-finding rate for these types.
Matching Matching is ...
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Applying the Martingale central limit theorem to the score process of an autoregressive model
This question is a natural continuation of the following question: How do I construct the score process of a Markov model and verify that it is a Martingale? In this problem, we set up as follows:
...
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Estimating excess probability
I have three players A,B,C, where C ideally functions as a baseline. They play different games (not against each other) and I can observe their win probability, for example P(A wins in game I) = 90%, ...
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In economics, what variables do we usually assume to follow an exponential distribution?
In economics, what variables do we usually assume to follow an exponential distribution? I would like as many examples as possible, and it would be great if you have a rationale(economic reason or ...
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Best-responding to a stochastically higher distribution of bids
In Auction Theory, Krishna writes that:
a bidder who faces a stochastically higher distribution of bids–in the
sense of reverse hazard rate dominance–will bid higher
(This follows the proof of ...
user17900
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Is maximal utility conditional on information linear in convex combinations of priors?
This is related to a Mathematica question here - https://math.stackexchange.com/q/1952779/374929
Is a (maximal expected utility) function of the form
$U(\mu, X) \equiv \int_\Theta \int_\mathcal{X} \...
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How to use Girsanov theorem to prove $\hat{W_t}$ is $\hat{\mathbb P}$-Brownian motion?
Assumptions:
Let $T > 0$, and let $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathbb P = \tilde{\mathbb P}$ (risk-neutral measure) and $...
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How can I construct a process for cumulative returns that is riskless?
This question is a little more specific than the title. Here I use the same notation that is set forth in this other question about cumulative returns (the sum of return observations). That is, let $...
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Probability for Economics
I need to learn ASAP on the list of topics: Multivariate Distribution, discrete and continuous random variables; integration and expectation; law of large numbers and central limit theorem, confidence ...
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What does this notation mean?
I am following an IO paper and, at some point, a function $h(\cdot)\in \mathbb{R}^2_+$ is defined as
$$h(t) = \cases{\mathbb{1}(t=k)*|\mathbb{N}(0,1)|\\\mathbb{1}(t<k)*|\mathbb{N}(0,1)|}$$ where $k\...
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Finding the risk attitude parameter in a CPT Risk Elicitation Model
I'm working with this article by Bauermeister et al. that compares the risk attitude parameters found using two different risk elicitation models. The models each use a series of gambling options to ...
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Bayesian update in the beliefs about the signals
Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
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Question on the choice of boundary in the CUSUM test when we make some resampling
Question on the choice of boundary in the CUSUM test when we make some resampling
We are considering to make a CUSUM test for some economical time series $𝑋=(𝑥_1,..,x_n)$. Suppose 𝑋 contains many ...
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Assessing risk in a decision problem with repeated toss
The problem starts at time t0.
At each time step, the participant can choose to opt out and claim a loser's reward Rl.
At each time step, the participant has a probability p to win a winner's reward ...
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Global games: How to derive posterior with uniform prior and signal
I have access to some lecture notes on Global games (following the model of Carlsson and van Damme (1993)) showing how to derive the players posterior beliefs. But I don't really grasp how players ...
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Expectation conditional on a sum of random variables
The setting is a simple OLS regression where the true model has regressor $x$ and error term $u$, but we can only measure $\bar{x}=x+v$ where $v$ is iid with mean 0.
According to the textbook:
$\...
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How to determine the default probability of a county in a bond that is not in its native currency?
Consider the following case:
Country P uses the currency Euro and gives p percent interest on a one year bond issued in Euro.
Country Q uses the currency TL and gives q percent interest on a one ...
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Marital status determinants
I am looking for the researches that have studied factors influencing marital status probability. I need them for citation purposes. After looking for a long time I have not found anything. So I need ...
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Can't solve this matrix for Nash Equilibrium?
So, I have the following 9 by 9 probability matrix. I want to solve it for a nash equilibrium.
https://docs.google.com/spreadsheets/d/16Y1FqxRIAHsHpgEz1ckxDt2sEOInOG3zz_wU8kBHvB4/edit?usp=sharing
For ...
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References about market sampling
Suppose the government wants to determine the efficient price of a certain commodity for which there is no competitive market. One way to do this is to take a sample of the potential buyers and ask ...
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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 ...
user6717
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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 ...
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transition probabilities from a AR(1) stochastic process
I have a stochastic volatility model for commodity price which follows an AR(1) process:
ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1)
σt − μ = ρσ(σt−1 − μ) + ηεt εt ∼ IID(0, 1)
...
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The most used probability distributions in moral hazard models?
I'm engaged in making a variation of the canonical moral hazard model, but I need some examples of probability distributions to make some simulations and graphs. What are the probability distributions ...
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Rate of convergence and asymptotic dominance in $\Vert x \Vert \gg \Vert(\hat\beta-\beta)\cdot u\Vert $
Let $\Vert A \Vert$ denote the spectral norm of a random matrix. Let $x$ and $u_k$ be N$\times$T matrices. Denote $\beta \cdot u = \sum_{k=1}^K\beta_ku_k $, where $\beta$ is a K-vector and $\beta_k$ a ...
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