A formal S4 class representation of Sparre Andersen's extension that includes capital injections.
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.
capital_injection_interarrival_generatora function indicating the random generator of capital injections' interarrival times.
capital_injection_interarrival_parametersa named list containing parameters for the random generator of capital injections' interarrival times.
capital_injection_size_generatora function indicating the random generator of capital injections' sizes.
capital_injection_size_parametersa named list containing parameters for the random generator of capital injections' sizes.
The model is defined as follows:
$$X_(t) = u + ct + \sum_{k=1}^{N^{(+)}(t)} Y^{(+)}_k -
\sum_{i=1}^{N^{(-)}(t)} Y^{(-)}_i$$
where \(u\) is the initial capital (initial_capital), \(c\) is the
premium rate (premium_rate), \(N^{(+)}(t)\) is the renewal process
of positive jumps (capital injections) defined by distribution of
interarrival times (capital_injection_interarrival_generator and
capital_injection_interarrival_parameters), \(Y^{(+)}_k\) are iid
capital injections' sizes (capital_injection_size_generator
and capital_injection_size_parameters), \(N^{(-)}(t)\) is the
renewal process of claims 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
SparreAndersenCapitalInjections.
Breuera L., Badescu A. L. A generalised Gerber Shiu measure for Markov-additive risk processes with phase-type claims and capital injections. Scandinavian Actuarial Journal, 2014(2): 93-115, 2014.