Stable-1/2 bridges and insurance

Edward Hoyle, Lane P. Hughston, and Andrea Macrina. "Stable-1/2 bridges and insurance." Banach Center Publications 104.1 (2015): 95-120. <http://eudml.org/doc/282480>.

@article{EdwardHoyle2015,
abstract = {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.},
author = {Edward Hoyle, Lane P. Hughston, Andrea Macrina},
journal = {Banach Center Publications},
keywords = {stable- bridges; insurance; best-estimate ultimate loss process},
language = {eng},
number = {1},
pages = {95-120},
title = {Stable-1/2 bridges and insurance},
url = {http://eudml.org/doc/282480},
volume = {104},
year = {2015},
}

TY - JOUR
AU - Edward Hoyle
AU - Lane P. Hughston
AU - Andrea Macrina
TI - Stable-1/2 bridges and insurance
JO - Banach Center Publications
PY - 2015
VL - 104
IS - 1
SP - 95
EP - 120
AB - 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.
LA - eng
KW - stable- bridges; insurance; best-estimate ultimate loss process
UR - http://eudml.org/doc/282480
ER -