# Questions tagged [probability]

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### Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
249 views

### Probability density function of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
89 views

### How to derive the CDF and the probability density function [closed]

Is there something missing in this question i dont seem to understand, can anyone help explaining what is required?
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### Event Occurs Almost Surely

Consider an uncountably infinite space, an infinite coin-tossing. Let $(\Omega,\mathcal{F},\mathbb{P})$ be the probability space. If a set $A\in\mathcal{F}$ satisfies $\mathbb{P(A)=1},$ then we say ...
213 views

### Geometric Brownian Motion - Price Probabilities

I am modeling a stock price that follows Geometric Brownian Motion and have the following: $E(X)$ = .16 (16%) $\sigma$ = .24 (24%) $X_0$ = 95 $T$ = 1 (12 months) I am trying to find the ...
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### Produce the random variable for an asset from a uniformly distributed random varible

I'm working on a quant interview question from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors). I cannot understand the following question(not the answer, ...
74 views

### Introducting a new probability measure

I'm trying to understand what means : $$\frac {d \mathbb {\tilde{P}} }{d \mathbb P } \bigg\rvert_{\mathcal F_t }$$where $\mathcal F_t$ is a filtration I guess (not explicitely mentionned). they ...
64 views

### Excel formula for Laplace distribution

I am trying to create a forecast model, projecting the number of passengers through an airport over a period of time (daily, weekly, and monthly). I've already used Excel's FORECAST and POISSON ...
215 views

### Probability Density Function of a Wiener Process Minimum

Let $W_t$ be a standard Wiener process. Find the probability density function of $m_T = min_{t\in [0,T ]}W_t$. I know that it is based of the concept of the reflection principle, but I wasn't too ...
870 views

### probability question about brownian motion

Assume $W_{t}$ is a standard Brownian Motion, calculate the the probability that $W_{t}*W_{2t}$ is negative, i.e., $P(W_{t}*W_{2t}<0)$. I find it tricky to calculate the probability.Thank you.
188 views

### Arithmetic Brownian Motion in Market Making papers

We often consider high-frequency market maker and suppose that the reference price is the arithmetic Brownian Motion: $dS_{t} = \sigma d W_t$ What is the difference $t_n - t_{n-1}$ in this case? Is ...
76 views

### Intuitive explanation of why ITM options have low Time/Extrinsic Values?

While brushing up on my knowledge about the Greeks, I have been struggling coming up with an intuitive, probability-based explanation behind why not only Out-of-the-Money (OTM), but also In-the-Money (...
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### How is the “probabilities sum to $1$” rule enforced in betting exchanges?

Suppose that I am interested in a market on a betting exchange for the outright winner of some event, with three competitors, $A, B$ and $C$ with corresponding probabilities of winning $a, b$ and $c$. ...
2k views

### Box-Muller Method Proof

Here we want to show that the Box-Muller method generates a pair of independent standard Gaussian random variables. But I don't understand why we use the determinant? For me when you have two ...
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### Need help figuring out probability that price will be touched in a specific time period

I have a formulas for figuring out probability the price will be struck within T days. Now what I need help with is figuring out the probability price will be stuck with in a given (T) minutes, or (T) ...
132 views

### Importance of filtrations that are NOT natural filtrations

I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional ...