Based on the compound Poisson risk process that is perturbed by
a Brownian motion, saddlepoint approximations to some measures of risk are
provided. Various approximation methods for the probability of ruin are
also included. Furthermore, exact values of both the risk measures as well
as the probability of ruin are available if the individual claims follow
a hypo-exponential distribution (i. e., if it can be represented as a sum
of independent exponentially distributed random variables with different
rate parameters). For more details see Gatto and Baumgartner (2014)
Known Issues and Limitations
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The approximation of the probability of ruin using the method of
upper and lower bounds does not provide the correct results if the
integrated tail area distribution function is not supplied. More
specifically, the less accurate bounds avoiding integration are not yet
correctly implemented.
Models without oscillation are currently not supported. At the
moment, there is no guarantee that the functions provided in this
package provide sensible output (or, for that matter, any output at all)
if variance = 0.