Simulasi Ruin Probability Perusahaan Asuransi dengan Analisis Sensitivitas Premi, Jumlah Pelanggan dan Frekuensi Klaim

Abstract

Insurance plays a crucial role in maintaining financial stability for individuals, companies, and the economy. However, simultaneous claims can increase the risk of insurer bankruptcy. This study analyzes the probability of insurance company bankruptcy through a simulation based on the classical surplus model. The surplus is modeled as a function of initial capital, premium income, and claims, where claim numbers follow a Poisson distribution and claim sizes follow an Exponential distribution. Simulations were conducted in Python with parameters including initial capital of IDR 10 billion, daily premiums of IDR 3,000–IDR 4,000, customers ranging from 180,000 to 219,981, daily claim frequency (λ) of 2,128–2,500, a one-year observation period, and 500 iterations per scenario. Results show that premiums below IDR 3,600 lead to bankruptcy with an average survival time of less than 250 days. Conversely, premiums of IDR 3,600 or higher allow survival throughout the observation period. Sensitivity analysis indicates that customer numbers and claim frequency strongly affect financial stability. Under declining customers or increasing claims, IDR 3,600 is no longer sufficient. Therefore, optimal premium determination should account for realistic operational variations to ensure insurance company sustainability.