Simulation from Compound Hierarchical Models
Simulate data for insurance applications allowing hierarchical structures and separate models for the frequency and severity of claims distributions.
rcomphierarc is an alias for simul.
simul(nodes, model.freq = NULL, model.sev = NULL, weights = NULL) rcomphierarc(nodes, model.freq = NULL, model.sev = NULL, weights = NULL) ## S3 method for class 'portfolio' print(x, ...)
nodes |
a vector or a named list giving the number of "nodes" at each level in the hierarchy of the portfolio. The nodes are listed from top (portfolio) to bottom (usually the years of experience). |
model.freq |
a named vector of expressions specifying the
frequency of claims model (see details); if |
model.sev |
a named vector of expressions specifying the severity
of claims model (see details); if |
weights |
a vector of weights. |
x |
a |
... |
potential further arguments required by generic. |
The order and the names of the elements in nodes,
model.freq and model.sev must match. At least one of
model.freq and model.sev must be non NULL.
nodes may be a basic vector, named or not, for non hierarchical
models. The rule above still applies, so model.freq and
model.sev should not be named if nodes is not. However,
for non hierarchical models, rcompound is faster and has
a simpler interface.
nodes specifies the hierarchical layout of the portfolio. Each
element of the list is a vector of the number of nodes at a given
level. Vectors are recycled as necessary.
model.freq and model.sev specify the simulation models
for claim numbers and claim amounts, respectively. A model is
expressed in a semi-symbolic fashion using an object of mode
expression. Each element of the object
must be named and should be a complete call to a random number
generation function, with the number of variates omitted. Hierarchical
(or mixtures of) models are achieved by replacing one or more
parameters of a distribution at a given level by any combination of
the names of the levels above. If no mixing is to take place at a
level, the model for this level can be NULL.
The argument of the random number generation functions for the number
of variates to simulate must be named n.
Weights will be used wherever the name "weights" appears in a
model. It is the user's responsibility to ensure that the length of
weights will match the number of nodes when weights are to be
used. Normally, there should be one weight per node at the lowest
level of the model.
Data is generated in lexicographic order, that is by row in the output matrix.
An object of class "portfolio". A
print method for this class displays the models used in the
simulation as well as the frequency of claims for each year and entity
in the portfolio.
An object of class "portfolio" is a list containing the
following components:
data |
a two dimension list where each element is a vector of claim amounts; |
weights |
the vector of weights given in argument reshaped as a
matrix matching element |
classification |
a matrix of integers where each row is a unique set of subscripts identifying an entity in the portfolio (e.g. integers i, j and k for data X[ijkt]); |
nodes |
the |
model.freq |
the frequency model as given in argument; |
model.sev |
the severity model as given in argument. |
It is recommended to manipulate objects of class "portfolio" by
means of the corresponding methods of functions aggregate,
frequency and severity.
Vincent Goulet vincent.goulet@act.ulaval.ca, Sébastien Auclair and Louis-Philippe Pouliot
Goulet, V. and Pouliot, L.-P. (2008), Simulation of compound hierarchical models in R, North American Actuarial Journal 12, 401–412.
simul.summaries for the functions to create the
matrices of aggregate claim amounts, frequencies and individual
claim amounts.
rcompound for a simpler and much faster way to generate
variates from standard, non hierarchical, compound models.
## Two level (contracts and years) portfolio with frequency model
## Nit|Theta_i ~ Poisson(Theta_i), Theta_i ~ Gamma(2, 3) and severity
## model X ~ Lognormal(5, 1)
simul(nodes = list(contract = 10, year = 5),
model.freq = expression(contract = rgamma(2, 3),
year = rpois(contract)),
model.sev = expression(contract = NULL,
year = rlnorm(5, 1)))
## Model with weights and mixtures for both frequency and severity
## models
nodes <- list(entity = 8, year = c(5, 4, 4, 5, 3, 5, 4, 5))
mf <- expression(entity = rgamma(2, 3),
year = rpois(weights * entity))
ms <- expression(entity = rnorm(5, 1),
year = rlnorm(entity, 1))
wit <- sample(2:10, 35, replace = TRUE)
pf <- simul(nodes, mf, ms, wit)
pf # print method
weights(pf) # extraction of weights
aggregate(pf)[, -1]/weights(pf)[, -1] # ratios
## Four level hierarchical model for frequency only
nodes <- list(sector = 3, unit = c(3, 4),
employer = c(3, 4, 3, 4, 2, 3, 4), year = 5)
mf <- expression(sector = rexp(1),
unit = rexp(sector),
employer = rgamma(unit, 1),
year = rpois(employer))
pf <- simul(nodes, mf, NULL)
pf # print method
aggregate(pf) # aggregate claim amounts
frequency(pf) # frequencies
severity(pf) # individual claim amounts
## Standard, non hierarchical, compound model with simplified
## syntax (function rcompound() is much faster for such cases)
simul(10,
model.freq = expression(rpois(2)),
model.sev = expression(rgamma(2, 3)))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.