Estimation of Ruin Probabilities in an Extended Risk Model with Inhomogeneous Claim Counts and Financial Risks

Abstract

Classical ruin models commonly assume stationary claim arrivals and often examine financial conditions, taxation, and heavy-tailed losses separately. This fragmentation limits their ability to assess insurer solvency when claim frequency and economic conditions vary simultaneously. This study develops an extended risk framework that jointly incorporates an inhomogeneous Poisson claim-counting process, financial adjustment through the real force of accumulation, and proportional taxation. Ruin probabilities are examined under exponential and subexponential claim-size distributions. For exponential claims, the framework provides an analytical characterization of the effects of initial surplus, premium loading, financial adjustment, and taxation on insolvency risk. For subexponential claims, the asymptotic analysis shows that ruin is governed by the tail behaviour of exceptionally large losses. The results indicate that larger initial reserves and premium loadings strengthen solvency, whereas higher claim intensity and taxation increase ruin risk; heavy-tailed claims also produce more persistent insolvency exposure than light-tailed claims. The novelty of the study lies in integrating time-varying claim arrivals, financial risk, taxation, and contrasting claim-tail regimes within a single analytical structure. The proposed framework provides a basis for solvency assessment, capital planning, and actuarial risk management under changing insurance and economic conditions.