Cumulative Insurance Loss Payments
This dataset, discussed in Gesmann & Morris (2020), contains cumulative insurance loss payments over the course of ten years.
loss
A data frame of 55 observations containing information on the following 4 variables.
Origin year of the insurance (1991 to 2000)
Deviation from the origin year in months
Cumulative loss payments
Achieved premiums for the given origin year
Gesmann M. & Morris J. (2020). Hierarchical Compartmental Reserving Models. CAS Research Papers.
## 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)
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