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We study a Cox risk model that accounts for both, seasonal variations and random ﬂuctuations in the claims intensity. This occurs with natural phenomena that evolve in a seasonal environment and affect insurance claims, such as hurricanes.
More precisely, we deﬁne an intensity process, governed by a periodic function with a random peak level. The periodic intensity function follows a deterministic pattern in each short–term period, and is illustrated by a beta–type function. A two–state Markov chain deﬁnes the level process, explaining the random effect due to “high” or “low risk” years. This yields a regime–switching process, alternating between the two resulting intensities.
The properties of the corresponding claim counting process are discussed in detail. By properly deﬁning the Lundberg coefficient, Lundberg–typebounds for ﬁnite time ruin probabilities are derived.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Lu, Yi and Garrido, José|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 2/04|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Cox model; Non-homogeneous Poisson process; Regime–switching process; Periodicity; Lundberg–type bound; Ruin probability; Risk theory|
|Deposited By:||ANDREA MURRAY|
|Deposited On:||03 Jun 2010 15:32|
|Last Modified:||08 Dec 2010 18:27|
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