Abstract

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.