brms (version 2.16.1)

loss: Cumulative Insurance Loss Payments

Description

This dataset, discussed in Gesmann & Morris (2020), contains cumulative insurance loss payments over the course of ten years.

Usage

loss

Format

A data frame of 55 observations containing information on the following 4 variables.

AY

Origin year of the insurance (1991 to 2000)

dev

Deviation from the origin year in months

cum

Cumulative loss payments

premium

Achieved premiums for the given origin year

Examples

# NOT RUN {
# non-linear model to predict cumulative loss payments
fit_loss <- brm(
  bf(cum ~ ult * (1 - exp(-(dev/theta)^omega)),
     ult ~ 1 + (1|AY), omega ~ 1, theta ~ 1, 
     nl = TRUE),
  data = loss, family = gaussian(),
  prior = c(
    prior(normal(5000, 1000), nlpar = "ult"),
    prior(normal(1, 2), nlpar = "omega"),
    prior(normal(45, 10), nlpar = "theta")
  ),
  control = list(adapt_delta = 0.9)
)

# basic summaries
summary(fit_loss)
conditional_effects(fit_loss)

# plot predictions per origin year
conditions <- data.frame(AY = unique(loss$AY))
rownames(conditions) <- unique(loss$AY)
me_loss <- conditional_effects(
  fit_loss, conditions = conditions, 
  re_formula = NULL, method = "predict"
)
plot(me_loss, ncol = 5, points = TRUE)
# }
# NOT RUN {
# }