ruin {actuar}  R Documentation 
Calulation of infinite time probability of ruin in the models of CramÃ©rLundberg and Sparre Andersen, that is with exponential or phasetype (including mixtures of exponentials, Erlang and mixture of Erlang) claims interarrival time.
ruin(claims = c("exponential", "Erlang", "phasetype"), par.claims, wait = c("exponential", "Erlang", "phasetype"), par.wait, premium.rate = 1, tol = sqrt(.Machine$double.eps), maxit = 200L, echo = FALSE) ## S3 method for class 'ruin' plot(x, from = NULL, to = NULL, add = FALSE, xlab = "u", ylab = expression(psi(u)), main = "Probability of Ruin", xlim = NULL, ...)
claims 
character; the type of claim severity distribution. 
wait 
character; the type of claim interarrival (wait) time distribution. 
par.claims, par.wait 
named list containing the parameters of the distribution (see details). 
premium.rate 
numeric vector of length 1; the premium rate. 
tol, maxit, echo 
respectively the tolerance level of the
stopping criteria, the maximum number of iterations and whether or
not to echo the procedure when the transition rates matrix is
determined iteratively. Ignored if 
x 
an object of class 
from, to 
the range over which the function will be plotted. 
add 
logical; if 
xlim 
numeric of length 2; if specified, it serves as default
for 
xlab, ylab 
label of the x and y axes, respectively. 
main 
main title. 
... 
further graphical parameters accepted by

The names of the parameters in par.claims
and par.wait
must the same as in dexp
,
dgamma
or dphtype
, as appropriate.
A model will be a mixture of exponential or Erlang distributions (but
not phasetype) when the parameters are vectors of length > 1
and the parameter list contains a vector weights
of the
coefficients of the mixture.
Parameters are recycled when needed. Their names can be abbreviated.
Combinations of exponentials as defined in Dufresne and Gerber (1988) are not supported.
Ruin probabilities are evaluated using pphtype
except
when both distributions are exponential, in which case an explicit
formula is used.
When wait != "exponential"
(Sparre Andersen model), the
transition rate matrix Q of the distribution of
the probability of ruin is determined iteratively using a fixed
pointlike algorithm. The stopping criteria used is
max(rowSum(Q  Q')) < tol,
where Q and Q' are two successive values of the matrix.
A function of class "ruin"
inheriting from the
"function"
class to compute the probability of ruin given
initial surplus levels. The function has arguments:
u 
numeric vector of initial surplus levels; 
survival 
logical; if 
lower.tail 
an alias for 
Vincent Goulet vincent.goulet@act.ulaval.ca, and Christophe Dutang
Asmussen, S. and Rolski, T. (1991), Computational methods in risk theory: A matrix algorithmic approach, Insurance: Mathematics and Economics 10, 259–274.
Dufresne, F. and Gerber, H. U. (1988), Three methods to calculate the probability of ruin, Astin Bulletin 19, 71–90.
Gerber, H. U. (1979), An Introduction to Mathematical Risk Theory, Huebner Foundation.
## Case with an explicit formula: exponential claims and exponential ## interarrival times. psi < ruin(claims = "e", par.claims = list(rate = 5), wait = "e", par.wait = list(rate = 3)) psi psi(0:10) plot(psi, from = 0, to = 10) ## Mixture of two exponentials for claims, exponential interarrival ## times (Gerber 1979) psi < ruin(claims = "e", par.claims = list(rate = c(3, 7), w = 0.5), wait = "e", par.wait = list(rate = 3), pre = 1) u < 0:10 psi(u) (24 * exp(u) + exp(6 * u))/35 # same ## Phasetype claims, exponential interarrival times (Asmussen and ## Rolski 1991) p < c(0.5614, 0.4386) r < matrix(c(8.64, 0.101, 1.997, 1.095), 2, 2) lambda < 1/(1.1 * mphtype(1, p, r)) psi < ruin(claims = "p", par.claims = list(prob = p, rates = r), wait = "e", par.wait = list(rate = lambda)) psi plot(psi, xlim = c(0, 50)) ## Phasetype claims, mixture of two exponentials for interarrival times ## (Asmussen and Rolski 1991) a < (0.4/5 + 0.6) * lambda ruin(claims = "p", par.claims = list(prob = p, rates = r), wait = "e", par.wait = list(rate = c(5 * a, a), weights = c(0.4, 0.6)), maxit = 225L)