We develop a class of non-life reserving models using a stable-1/2 random
bridge to simulate the accumulation of paid claims, allowing for an essentially
arbitrary choice of a priori distribution for the ultimate loss. Taking an
information-based approach to the reserving problem, we derive the process of
the conditional distribution of the ultimate loss. The "best-estimate ultimate
loss process" is given by the conditional expectation of the ultimate loss. We
derive explicit expressions for the best-estimate ultimate loss process, and
for expected recoveries arising from aggregate excess-of-loss reinsurance
treaties. Use of a deterministic time change allows for the matching of any
initial (increasing) development pattern for the paid claims. We show that
these methods are well-suited to the modelling of claims where there is a
non-trivial probability of catastrophic loss. The generalized inverse-Gaussian
(GIG) distribution is shown to be a natural choice for the a priori ultimate
loss distribution. For particular GIG parameter choices, the best-estimate
ultimate loss process can be written as a rational function of the paid-claims
process. We extend the model to include a second paid-claims process, and allow
the two processes to be dependent. The results obtained can be applied to the
modelling of multiple lines of business or multiple origin years. The
multi-dimensional model has the property that the dimensionality of
calculations remains low, regardless of the number of paid-claims processes. An
algorithm is provided for the simulation of the paid-claims processes.Comment: To appear in: Advances in Mathematics of Finance (A. Palczewski and
L. Stettner, editors.), Banach Center Publications, Polish Academy of
Science, Institute of Mathematic