CramerLundbergCapitalInjections {ruin} | R Documentation |
Constructs an object of CramerLundbergCapitalInjections S4 class
Description
CramerLundbergCapitalInjections()
constructs an object of
CramerLundbergCapitalInjections
S4 class.
Usage
CramerLundbergCapitalInjections(initial_capital = NULL, premium_rate = NULL,
claim_poisson_arrival_rate = NULL, claim_size_generator = NULL,
claim_size_parameters = NULL, capital_injection_poisson_rate = 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: |
premium_rate |
a length one numeric non-negative vector specifying a
premium rate. Default: |
claim_poisson_arrival_rate |
a length one numeric positive vector
specifying the rate of the Poisson process of claims' arrivals. Default:
|
claim_size_generator |
a function indicating the random generator of
claims' sizes. Default: |
claim_size_parameters |
a named list containing parameters for the
random generator of claims' sizes. Default: |
capital_injection_poisson_rate |
a length one numeric positive vector
specifying the rate of the Poisson process of capital injections' arrivals.
Default: |
capital_injection_size_generator |
a function indicating the random
generator of capital injections' sizes. Default: |
capital_injection_size_parameters |
a named list containing parameters
for the random generator of capital injections' sizes. Default:
|
Details
The function constructs an object of a formal S4 class
CramerLundbergCapitalInjections
, a representation of an extension of
Cramer-Lundberg 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 Poisson process
of positive jumps (capital injections) with intensity \lambda^{(+)}
(capital_injection_poisson_rate
), Y^{(+)}_k
are
iid capital injections' sizes (capital_injection_size_generator
and capital_injection_size_parameters
), N^{(-)}(t)
is the
Poisson process of negative jumps (claims) with intensity \lambda^{(-)}
(claim_poisson_arrival_rate
), Y^{(-)}_i
are iid claim sizes
(claim_size_generator
and claim_size_parameters
).
Value
An object of CramerLundbergCapitalInjections 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
,
SparreAndersen
, link{SparreAndersenCapitalInjections}
.
Examples
model <- CramerLundbergCapitalInjections(
initial_capital = 10,
premium_rate = 1,
claim_poisson_arrival_rate = 1,
claim_size_generator = rexp,
claim_size_parameters = list(rate = 1),
capital_injection_poisson_rate = 1,
capital_injection_size_generator = rexp,
capital_injection_size_parameters = list(rate = 1)
)