To address the challenges of assessing bankruptcy costs and earnings volatility for insurance companies in a bounded risk environment, this paper proposes an analytical framework based on the specific Gerber-Shiu function of a bounded risk model. Firstly, based on the classic Gerber-Shiu function, a new and specific model suitable for bounded risk situations is constructed, and a risk ceiling factor is introduced to describe the insurance company’s defense ability when encountering extreme risks. Then, functional analysis and martingale method are used to deeply solve the specific function, and its analytical expression under bounded conditions is obtained. Finally, by analyzing the simulated data and historical data of actual insurance companies, the results show that the bankruptcy probability of the specific Gerber-Shiu model is lower than that of other models in high-risk scenarios. For example, when the initial surplus is positive, the bankruptcy probability of the model is about 0.05, which is lower than 0.06 of the generalized double Poisson model and 0.07 of the Lévy process model. At the same time, under the conditions of high loss limit, initial surplus, and high claim arrival rate, the bankruptcy cost expectations of the extended model are 8.5, 9.1, and 10.3, respectively, showing significant stability. The experiment verified the high adaptability of the specific Gerber-Shiu model under extreme risk conditions and provided insurance companies with a more reliable quantitative risk management support tool.