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

## TL;DR

This paper derives an asymptotic formula for the probability of ruin within a finite time horizon in a nonhomogeneous Poisson risk model with subexponential claims, considering conditional independence and random weights.

## Contribution

It provides new asymptotic results for ruin probabilities and weighted sums in nonhomogeneous Poisson risk models with subexponential claims.

## Key findings

- Asymptotic formula for finite-time ruin probability derived
- Relations for weighted sums of subexponential variables established
- Results applicable to risk management with nonhomogeneous claim processes

## 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 $\sum_{i=1}^n \theta_iX_i$, in which the weights $\theta_i$ $i=1,2,\cdots, n$ 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.