Derivation of A Risk Model that Incorporates Inhomogeneous Claim Counts and Financial Risks

Abstract

In the insurance industry, ruin or insolvency occurs when an insurer’s total liabilities exceed its assets, rendering it unable to meet future claims. Traditional ruin probability models, such as the Cramer-Lundberg model, assume a homogeneous Poisson claim process with a constant arrival rate, which may not accurately reflect real-world market dynamics. In practice, claim arrivals are often in-homogeneous due to seasonal variations, policyholder behaviors, and external economic factors. Additionally, financial risks including inflation, interest rates, and taxation further influence an insurer’s solvency. This study develops an extended risk model that incorporates in-homogeneous claim counts and financial risks, offering a more realistic framework for estimating ruin probabilities in non-life insurance. The proposed model is derived using integral-differential equations and Cramer-Lundberg approximations, providing a refined approach to risk assessment. The findings offer valuable insights for insurers and regulators in designing risk management strategies to mitigate insolvency risks and ensure financial stability.