# 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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### Solve for withdrawal rate in Monte Carlo simulation of retirement

I've been working with compound returns and distribution of wealth over time for quite some time now and I feel like I am hitting a wall. What am I trying to achieve? Imagine that you are about to ...
0answers
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### Exponential tilting for $E[1_{\{X > c\}}]$

Let's define $c \in \mathbb{R}$ and $X \sim N(0, 1)$. I want to define exponential tilting estimator for parameter $\delta := E[1_{\{X > c\}}]$. My work so far Exponential tilting is special case ...
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### Do I need to convert a data set into a probability distribution before feeding it into a Monte Carlo simulation?

I want to run a Monte Carlo simulation that, broadly speaking, converts a set of historical values into predicted future values. What is the best way to feed data into the simulation? Do I select ...
1answer
65 views

### Estimating the error function using Monte Carlo integration [closed]

How do I perform Monte Carlo integration on the error function $erf(x) = \frac{2}{\sqrt(\pi)}\int_{0}^{x}e^{-t^2}dt$ I have to estimate this using python but I'm not sure how the integral works at all....
0answers
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### Brownian motion with Karhunen-Loéve expansion

I try to simulate Brownian motion using Karhunen-Loéve expansion in R. I found that formula is: $$W_t=\sqrt2\sum_{k \ge0} \gamma_k\frac{2}{(2k+1)\pi}\sin\bigg(\bigg(k+\frac{1}{2}\bigg)\pi t\bigg)$$ I ...
0answers
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### What does it mean for the Monte Carlo Tree Search result to converge to the minimax algorithm result?

Consider a perfect information board game, where an outcome can be either a win or a loss. Suppose we try to find the best move using the Monte Carlo Tree Search and after many iterations the ...
0answers
23 views

### Can I exclude certain “bad” chains in an MCMC sampler? What are the implications?

I am using an ensemble MCMC sampler which samples from the posterior distribution in a Bayesian inversion. The sampler uses $N$ "chains" which all begin from different starting points drawn ...
1answer
295 views

### Monte-Carlo integration

Let a function $f$ to be $x\in \left[a,b\right],\:0\le f\left(x\right)\le c$. We want to calculate the approximation of the definite integral of the function in the range $[a,b]$, we can suppose that ...