The finite-time ruin probability of the nonhomogeneous Poisson risk model with conditionally independent subexponential claims

Abstract

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums ${\sum }_{i=1}^n{\theta }_i{X}_i,$ in which the weights θ_i $i=1,2,\cdots ,n$ are positive random variables which are bounded above and the primary random variables X_i, $i=1,2,\cdots ,n$ are conditionally independent and follow subexponential distributions.

Keywords:

• Conditionally independent
• nonhomogeneous Poisson process
• subexponential distributions
• finite-time ruin probabilities
• randomly weighted sums

AMS 2010 SUBJECT CLASSIFICATION:

• 62E20
• 62P05