🤖 AI Summary
This paper investigates the asymptotic behavior of the ruin probability under a risk model featuring stochastic premium income and investment in a risky asset governed by geometric Brownian motion, focusing on the limiting regime as initial capital tends to infinity. Assuming the premium density admits a rational Laplace transform, the authors employ Laplace transform techniques, stochastic process modeling, and asymptotic analysis to establish, for the first time within a risk-investment framework, a rigorous asymptotic ruin theory for premium processes with rational Laplace structure. They derive an explicit exponential decay rate for the ruin probability and its first-order asymptotic expansion. The results quantitatively characterize the joint impact of asset volatility and premium-structure parameters on ruin risk, thereby providing novel theoretical foundations and quantitative tools for insurance asset allocation and solvency assessment.
📝 Abstract
This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability for large initial capital values is investigated.