Create Simulation in R - r

Question

I have following problem:
A casualty insurance company has 1000 policyholders, each of whom will
independently present a claim in the next month with probability 5%.
Assuming that the amounts of the claims made are independent exponential
random variables with mean 800 Dollars.
Does anyone know how to create simulation in R to estimate the probability
that the sum of those claims exceeds 50,000 Dollars?

Answer 1

This sounds like a homework assignment, so it's probably best to consult with your teacher(s) if you're unsure about how to approach this. Bearing that in mind, here's how I'd go about simulating this:
First, create a function that generates values from an exponential distribution and sums those values, based on the values you give in your problem description.
get_sum_claims <- function(n_policies, prob_claim, mean_claim) {
sum(rexp(n = n_policies*prob_claim, rate = 1/mean_claim))
}
Next, make this function return the sum of all claims lots of times, and store the results. The line with map_dbl does this, essentially instructing R to return 100000 simulated sums of claims from the get_sum_claims function.
library(tidyverse)
claim_sums <- map_dbl(1:100000, ~ get_sum_claims(1000, 0.05, 800))
Finally, we can calculate the probability that the sum of claims is greater than 50000 by using the code below:
sum(claim_sums > 50000)/length(claim_sums)
This gives a fairly reliable estimate of ~ 0.046 as the probability that the sum of claims exceeds 50000 in a given month.

Answer 2

I'm a bit inexperienced with R, but here is my solution.
First, construct a function which simulates a single trial. To do so, one needs to determine how many claims are filed n. I hope it is clear that n ~ Binomial(1000, 0.05). Note that, you cannot simply assume n = 1000 * 0.05 = 50. By doing so, you would decrease the variance, which will result in a lower probability. I can explain why this is the case if needed. Then, generate and sum n values based on an exponential distribution with mean 800.
simulate_total_claims <- function(){
claim_amounts <- rexp(rbinom(n=1,size=1000, prob = 0.05), rate = 1/800)
total <- sum(claim_amounts)
return(total)
}
Now, all that needs to be done is run the above function a lot and determine the proportion of runs which have values greater than 50000.
totals <- rerun(.n = 100000, simulate_total_claims())
estimated_prob <- mean(unlist(totals) > 50000)