Untitled

Encyclopedia of Actuarial Science

2004

Subexponential distributions are a special class of heavy‐tailed distributions. The name arises from one of their properties that their tails decrease slower than any exponential tail (3). This implies that large values can occur in a sample with nonnegligible probability, which makes the subexponential distributions natural candidates for modeling situations in which some extremely large values occur in a sample compared with the mean size of the data. Such a pattern is often seen in insurance data, for instance, in fire, wind–storm, or flood insurance (collectively known as catastrophe insurance). Subexponential claims can account for large fluctuations in the surplus process of a company, increasing the risk involved in such portfolios.

Subexponential Distributions

Goldie¹,

Encyclopedia of Actuarial Science

2004

Large Insurance Losses Distributions

Fasen¹,

Encyclopedia of Quantitative Risk Analysis and Assessment

2008

Large insurance losses happen infrequently, but they happen. In this paper we present the standard distribution models used in fire, wind–storm, or flood insurance. We also present the Cramér–Lundberg model for the total claim amount and some more recent extensions. The classical insurance risk measure is the ruin probability, and we give a full account of the ruin event in such models. Finally, we present some results for an integrated insurance risk model, where investment risk is also taken into account.

Large Insurance Losses Distributions

Fasen¹,

Wiley StatsRef: Statistics Reference Online

2014

Self Cite

Large insurance losses happen infrequently, but they happen. In this paper we present the standard distribution models used in fire, wind-storm or flood insurance. We also present the classical Cramér-Lundberg model for the total claim amount and some more recent extensions. The classical insurance risk measure is the ruin probability and we give a full account of the ruin event in such models. Finally, we present some results for an integrated insurance risk model, where also investment risk is taken into account.