loss {brms}

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

Source

Gesmann M. & Morris J. (2020). Hierarchical Compartmental Reserving Models. CAS Research Papers.

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)

## End(Not run)