Description Details Slots References See Also
A formal S4 class representation of Cramer-Lundberg's extension that includes capital injections.
The model is defined as follows:
X_(t) = u + ct + ∑_{k=1}^{N^{(+)}(t)} Y^{(+)}_k - ∑_{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 λ^{(+)}
(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 λ^{(-)}
(claim_poisson_arrival_rate
), Y^{(-)}_i are iid claim sizes
(claim_size_generator
and claim_size_parameters
).
Objects of class can be created only by using the constructor
CramerLundbergCapitalInjections
.
initial_capital
a length one numeric non-negative vector specifying an initial capital.
premium_rate
a length one numeric non-negative vector specifying a premium rate.
claim_poisson_arrival_rate
a length one numeric positive vector specifying the rate of the Poisson process of claims' arrivals.
claim_size_generator
a function indicating the random generator of claims' sizes.
claim_size_parameters
a named list containing parameters for the random generator of claims' sizes.
capital_injection_poisson_rate
a length one numeric positive vector specifying the rate of the Poisson process of capital injections' arrivals.
capital_injection_size_generator
a function indicating the random generator of capital injections' sizes.
capital_injection_size_parameters
a named list containing parameters for the random generator of capital injections' sizes.
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.
CramerLundbergCapitalInjections
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