A formal S4 class representation of classical Sparre Andersen model.
initial_capitala length one numeric non-negative vector specifying an initial capital.
premium_ratea length one numeric non-negative vector specifying a premium rate.
claim_interarrival_generatora function indicating the random generator of claims' interarrival times.
claim_interarrival_parametersa named list containing parameters for the random generator of claims' interarrival times.
claim_size_generatora function indicating the random generator of claims' sizes.
claim_size_parametersa named list containing parameters for the random generator of claims' sizes.
The model is defined as follows:
$$X(t) = u + ct - \sum_{i=1}^{N(t)} Y_i,$$
where \(u\) is the initial capital (initial_capital), \(c\) is the
premium rate (premium_rate), \(N(t)\) is the renewal process defined
by distribution of interarrival times (claim_interarrival_generator
and claim_interarrival_parameters), \(Y_i\) are iid claim sizes
(claim_size_generator and claim_size_parameters).
Objects of class can be created only by using the constructor
SparreAndersen.
Andersen, E. Sparre. On the collective theory of risk in case of contagion between claims. Transactions of the XVth International Congress of Actuaries, 2(6), 1957.
Thorin O. Some Comments on the Sparre Andersen Model in the Risk Theory. ASTIN Bulletin: The Journal of the IAA, 8(1):104-125, 1974.