# Questions tagged [monte-carlo]

Questions on Monte Carlo methods, methods that require the repeated generation of pseudo- or quasi-random numbers for computing their results.

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### Is integration in high dimensions hard?

Consider the problem of estimating the integral $\int_{[0,1]^d} {\rm d}^dx f(x)$ where $f : [0,1]^d \to [a,b]$, to within relative error $\epsilon > 0$. My intuition is that this is an extremely ...
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### Calculate RTP value in slots machines using Monte carlo simulations

Could you explain me how to use Monte Carlo simulation to calculate RTP in slots. I have found this sentence on the internet but without any explanations. For obtained RTP Monte-Carlo simulation is ...
51 views

### $x_1^2+x_2^2+x_3^2+…x_{10}^2 \leq1$ Do I use the Mathematica QuasiMonteCarlo method wrongley?

I want to find the volume of the multisphere restricted by $x_1^2+x_2^2+x_3^2+...x_{10}^2 \leq1$, by using NIngtegrate and the QuasiMonteCarlo method. I start with dim = 10 with the expression ...
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### A question on hypercubes and the central limit theorem

I was reading a book on Monte Carlo methods and now I'm trying to make sense of an excercise. At one point they say that according to the central limit theorem most of the points ${\bf x} \in [0,1]^d$ ...
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### PDF of $Q$ Random Variable

Let $X\sim N(0,25)$, $Y\sim N(10,100)$, $Z\sim N(-10,50)$ and $Q=\tan^{-1}\left(\frac{Z}{\sqrt {X^2+Y^2}}\right)$ When I simulate $Q$ random variable with Monte Carlo method, I'm getting this ...
21 views

### Computing a “Double Conditional Distribution”

This question comes in the context of Gibbs sampling, and I have posted it on the Stats Stack Exchange. Let us say we are considering random vectors in $\mathbb{R}^2$ of the form $(X,Y)^T$, such that:...
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### Correctness of the following expected value

Let's say we have two functions f(x) and g(x), and we want to calculate the integral of the sum $\int f(x) + g(x)dx$ (the integral is finite) To do that, we randomly sample f(x) and g(x) with a ...
25 views

### Estimating Catalan numbers using Monte Carlo method

This question regards the classical problem of estimating Catalan numbers by performing a random walk on a grid of $n\times n$ squares. I will dectribe the problem for those who are not familiar with ...
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### Lognormal VaR vs. Normal VaR

I understand that the normal and lognormal VaR have different formulas. My question is can there be a general statement made i.e. is the normal VaR larger or smaller in general for example for ...
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### Monte Carlo Sampling with non-uniform distributions?

I'm currently studying Monte Carlo sampling, referencing Veach's "Robust Monte Carlo Methods for Light Transport Simulation". On page 63, he writes: The idea of Monte Carlo integration is to ...
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### Cointegration of the xt and yt and the distribution of the test statistic

So I'm trying to solve the following question: I've managed to answer the first part of the question (which involved explaining the whole process) and I know that the test isn't following a standard ...
37 views

### Monte Carlo and Sampling

Suppose that we have a finite state space $E$ and a distribution $\pi:E \rightarrow (0,1)$ with $\pi(x) >0$. The idea behind Monte Carlo is that we generate a Markov chain $X=(X_n,n\in \mathbb{N})$ ...
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### Lognormal distribution bounds on monte carlo simulation

As the lognormal distribution imposes bounds of attainable correlations as discussed in https://stats.stackexchange.com/questions/41734/attainable-correlations-for-lognormal-random-variables my ...
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### Markov chain Monte Carlo with stopping time

I'm doing my thesis where I'm required to compute the numerical value in the following problem: Let $(X_t)$ be a continuous-time Markov chain such that $X_0 = a$ almost surely. The state space $V$ ...
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### Monte Carlo Minimum Variance Hedge Ratio

So I was running a monte carlo simulation for two assets and a portfolio consisting of 1 quantity of the first asset and short a fraction x of the second asset to hedge, where the fraction is ...
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### Ratio of Normal Distribution probabilities

I am aware that the CDF of normal distributions are highly complex, but I have the following question. I have two normally distributed variables, A and B, ($N(\mu_A,\sigma_A$ and $N(\mu_B,\sigma_B$)); ...
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### Minimum Variance Hedge Ratio and Risk capital

I understand that the minimum variance hedge ratio minimizes the second moment of the portfolios. My question is how is it related to the size of the risk capital (which is calculated as the Value at ...
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### Steps to do a Monte Carlo simulation

I'm trying to do a Monte Carlo simulation but I'm lost in the process. The big question I want to answer is what's the probability I have to do a certain amount of work. In my solution I've already ...
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### Monte Carlo estimate for PI

Two well-known ways of estimating $\pi$ with Monte Carlo are dart throwing and Buffon's needle. Is there a MC experiment to estimate $\sqrt{\pi}$ at the usual rate of convergence?
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### Attainable correlation bounds of two log-normal random variables

McNeill et al. (2015) mention that the attainable correlation for two lognormal random variables are not between 1 and -1 as they are not of the same type. Now I was wondering since the minimum ...
The question is: Using Monte Carlo method, compute $\int_{0}^{1} \int_{-1}^{1} (x+y) dx dy.$ My resolution until now: Let $g = x+y$. $\Theta = E[g(U_{1}, ..., U_{n})]; U{1}, ..., U_{n}$ random ...