actuar (version 0.9-3)

simpf: Simulation of a portfolio of data

Description

simpf simulates data for insurance applications allowing hierarchical structures and separate models for the frequency and severity of claims distributions.

Usage

simpf(nodes, model.freq = NULL, model.sev = NULL, weights = NULL)
## S3 method for class 'simpf':
print(x, \dots)

Arguments

nodes

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 NULL, only claim amounts are simulated.

model.sev

a named vector of expressions specifying the severity of claims model (see details); if NULL, only claim numbers are simulated.

weights

a vector of weights.

x

a simpf object.

...

potential further arguments required by generic.

Value

• An object of class "simpf". 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 "simpf" 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 data, or NULL;
• 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 nodes argument, appropriately recycled;
• 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 "simpf" by means of the corresponding methods of functions aggregate, frequency and severity.

Details

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 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 resposibility 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 is lexicographic order, that is by row in the output matrix.

References

Goulet, V. (2006), Credibility for severity revisited, North American Actuarial Journal 10, 49--62.

See Also

simpf.summaries for the functions to create the matrices of aggregate claim amounts, frequencies and individual claim amounts.

Examples

## Simple 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)
simpf(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
wit <- sample(2:10, 35, replace = TRUE)
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))
pf <- simpf(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 <- simpf(nodes, mf, NULL)
pf 				# print method
aggregate(pf) 			# aggregate claim amounts
frequency(pf)  			# frequencies
severity(pf)			# individual claim amounts