fMonteCarlo {tailloss}

Monte Carlo Simulations.

Description

Function to estimate the total losses via the Monte Carlo simulations.

Usage

fMonteCarlo(ELT, s, t = 1, theta = 0, cap = Inf, nsim = 10000,
  verbose = FALSE)

Arguments

ELT

Data frame containing two numeric columns. The column Loss contains the expected losses from each single occurrence of event. The column Rate contains the arrival rates of a single occurrence of event.

s

Scalar or numeric vector containing the total losses of interest.

t

Scalar representing the time period of interest. The default value is t = 1.

theta

Scalar containing information about the variance of the Gamma distribution: sd[X] = x * theta. The default value is theta = 0: the loss associated to an event is considered as a constant.

cap

Scalar representing the financial cap on losses for a single event, i.e. the maximum possible loss caused by a single event. The default value is cap = Inf.

nsim

Integer representing the number of Monte Carlo simulations. The default value is nsim = 10e3.

verbose

Logical, if TRUE returns 95% CB and raw sample. The default is verbose = FALSE.

Value

If verbose = FALSE the function returns a numeric matrix, containing in the first column the pre-specified losses s, and the estimated exceedance probabilities in the second column. If verbose = TRUE the function returns a numeric matrix containing four columns. The first column contains the losses s, the second column contains the estimated exceedance probabilities, the other columns contain the 95% confidence bands. The attributes of this matrix are a vector simS containing the simulated losses.

Examples

data(UShurricane)

# Compress the table to millions of dollars

USh.m <- compressELT(ELT(UShurricane), digits = -6)
EPC.MonteCarlo <- fMonteCarlo(USh.m, s = 1:40, verbose = TRUE)
EPC.MonteCarlo
par(mfrow = c(1, 2))
plot(EPC.MonteCarlo[, 1:2], type = "l", ylim = c(0, 1))
matlines(EPC.MonteCarlo[, -2], ylim = c(0, 1), lty = 2, col = 1)
# Assuming the losses follow a Gamma with E[X] = x, and Var[X] = 2 * x and cap = 5m
EPC.MonteCarlo.Gamma <- fMonteCarlo(USh.m, s = 1:40, theta = 2, cap = 5, verbose = TRUE)
EPC.MonteCarlo.Gamma
plot(EPC.MonteCarlo.Gamma[, 1:2], type = "l", ylim = c(0, 1))
matlines(EPC.MonteCarlo.Gamma[, -2], ylim = c(0,1), lty = 2, col = 1)
# Compare the two results:
par(mfrow = c(1, 1))
plot(EPC.MonteCarlo[, 1:2], type = "l", main = "Exceedance Probability Curve",
ylim = c(0, 1))
lines(EPC.MonteCarlo.Gamma[, 1:2], col = 2, lty = 2)
legend("topright", c("Dirac Delta", expression(paste("Gamma(",
alpha[i] == 1 / theta^2, ", ", beta[i] ==1 / (x[i] * theta^2), ")", " cap =", 5))),
lwd = 2, lty = 1:2, col = 1:2)