CramerLundbergCapitalInjections-class {ruin} | R Documentation |
A formal S4 class CramerLundbergCapitalInjections
Description
A formal S4 class representation of Cramer-Lundberg's extension that includes capital injections.
Details
The model is defined as follows:
where is the initial capital (
initial_capital
), is the
premium rate (
premium_rate
), is the Poisson process
of positive jumps (capital injections) with intensity
(
capital_injection_poisson_rate
), are
iid capital injections' sizes (
capital_injection_size_generator
and capital_injection_size_parameters
), is the
Poisson process of negative jumps (claims) with intensity
(
claim_poisson_arrival_rate
), are iid claim sizes
(
claim_size_generator
and claim_size_parameters
).
Objects of class can be created only by using the constructor
CramerLundbergCapitalInjections
.
Slots
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.
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
CramerLundbergCapitalInjections