Quantifying insurance risks: Monte Carlo simulations and capital requirements

Type of the article: Research ArticleAbstractThe increasing complexity of insurance risks within the Solvency II regulatory framework highlights the need for accurate quantitative tools to assess the capital adequacy of insurance companies and model extreme insurance events. This study aims to demonstrate how the R programming language can be effectively used to perform Monte Carlo simulations of aggregate losses and subsequently estimate the capital requirement for large claims within partial internal solvency models used by insurance companies. The research methodology is based on Monte Carlo simulation implemented in the R programming environment using the replicate function to generate thousands of stochastic scenarios of claim frequency and individual claim severity based on selected probability distributions. Using real data from non-life insurance, the model generates hundreds of thousands of simulated scenarios of aggregate losses and constructs an empirical distribution of total losses from which risk measures are estimated. The simulation results show that the generated distribution captures not only the typical development of claims but also rare extreme events, which allows the estimation of the capital required to cover large claims at high confidence levels. These results enable insurance companies to more accurately quantify underwriting risk, analyze potential catastrophic loss scenarios, and determine the level of capital required to maintain solvency. The results confirm that Monte Carlo simulations implemented in the R programming language represent an effective tool for modeling aggregate losses and support risk management and capital optimization within internal solvency models.AcknowledgmentThis paper was prepared within the framework of the VEGA research projects No. 1/0497/25 Implementation of innovative approaches in managing and modelling of risk in internal models of insurance companies and No. 1/0377/25 Innovative methods of enterprise risk management and their application in risk modelling and management.