SparreAndersenCapitalInjections {ruin}

Constructs an object of SparreAndersenCapitalInjections S4 class

Description

SparreAndersenCapitalInjections() constructs an object of SparreAndersenCapitalInjections S4 class.

Usage

SparreAndersenCapitalInjections(initial_capital = NULL, premium_rate = NULL,
  claim_interarrival_generator = NULL, claim_interarrival_parameters = NULL,
  claim_size_generator = NULL, claim_size_parameters = NULL,
  capital_injection_interarrival_generator = NULL,
  capital_injection_interarrival_parameters = NULL,
  capital_injection_size_generator = NULL,
  capital_injection_size_parameters = NULL)

Arguments

initial_capital

a length one numeric non-negative vector specifying an initial capital. Default: 0.

premium_rate

a length one numeric non-negative vector specifying a premium rate. Default: 1.

claim_interarrival_generator

a function indicating the random generator of claims' interarrival times. Default: rexp.

claim_interarrival_parameters

a named list containing parameters for the random generator of claims' interarrival times. Default: list(rate = 1).

claim_size_generator

a function indicating the random generator of claims' sizes. Default: rexp.

claim_size_parameters

a named list containing parameters for the random generator of claims' sizes. Default: list(rate = 1).

capital_injection_interarrival_generator

a function indicating the random generator of capital injections' interarrival times. Default: rexp.

capital_injection_interarrival_parameters

a named list containing parameters for the random generator of capital injections' interarrival times. Default: list(rate = 1).

capital_injection_size_generator

a function indicating the random generator of capital injections' sizes. Default: rexp.

capital_injection_size_parameters

a named list containing parameters for the random generator of capital injections' sizes. Default: list(rate = 1).

Details

The function constructs an object of a formal S4 class SparreAndersenCapitalInjections, a representation of an extension of Sparre Andersen model that allows for positive jumps and 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).

Value

An object of SparreAndersenCapitalInjections class.

References

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.

See Also

CramerLundberg, CramerLundbergCapitalInjections, link{SparreAndersen}.

Examples

model <- SparreAndersenCapitalInjections(
  initial_capital = 10,
  premium_rate = 1,
  claim_interarrival_generator = rexp,
  claim_interarrival_parameters = list(rate = 1),
  claim_size_generator = rexp,
  claim_size_parameters = list(rate = 1),
  capital_injection_interarrival_generator = rexp,
  capital_injection_interarrival_parameters = list(rate = 1),
  capital_injection_size_generator = rexp,
  capital_injection_size_parameters = list(rate = 1)
)