Quantifying insurance risks: Monte Carlo simulations and capital requirements
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Received December 15, 2025;Accepted April 14, 2026;Published May 12, 2026
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Author(s)Michal PálešLink to ORCID Index: https://orcid.org/0000-0003-1082-6669
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František SlaninkaLink to ORCID Index: https://orcid.org/0000-0002-3515-5585
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Zuzana Krátka
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Jitka MeluchováLink to ORCID Index: https://orcid.org/0000-0003-1280-3866
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Lenka SmažákováLink to ORCID Index: https://orcid.org/0009-0001-6817-1303
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DOIhttp://dx.doi.org/10.21511/ins.17(1).2026.09
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Article InfoVolume 17 2026, Issue #1, pp. 113-125
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Type of the article: Research Article
Abstract
The 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.
Acknowledgment
This 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.
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JEL Classification (Paper profile tab)G22, G32, C15
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References39
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Tables2
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Figures2
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- Figure 1. Standard formula Solvency II
- Figure 2. Partial internal model for large claims using Monte Carlo simulations
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- Table 1. Non-life underwriting risk model
- Table 2. Generation of aggregate claim values in R for various combinations of random variables N (claim count) and X (claim severity) distributions
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Conceptualization
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Data curation
Michal Páleš
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Formal Analysis
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Funding acquisition
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Investigation
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Methodology
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Project administration
Michal Páleš
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Resources
Michal Páleš, František Slaninka
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Software
Michal Páleš, František Slaninka
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Supervision
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Validation
Michal Páleš, František Slaninka, Zuzana Krátka, Jitka Meluchová, Lenka Smažáková
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Conceptualization
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Service quality, customers’ satisfaction, and profitability: an empirical study of Saudi Arabian insurance sector
Investment Management and Financial Innovations Volume 15, 2018 Issue #2 pp. 232-247 Views: 5595 Downloads: 1073 TO CITE АНОТАЦІЯFinancial performance is the fundamental aspect to test the performance of the companies. The performance of insurance sector, like any other service industry, is supposed to depend significantly on customers. When it comes to customers, it is an established fact that customer satisfaction would be an important element. Customer satisfaction primarily depends on the quality of service it gets. It can be safely hypothesized that better service quality would lead to higher satisfaction, which would ultimately lead to higher profits for the company. Studies on this relationship in the insurance sector for Saudi Arabia are missing. Hence, this study aims at studying both the profitability of companies and quality of service and tries to relate it to customer satisfaction. The results are quite surprising, as the study establishes that although the qualities of services are found wanting in many areas, companies are earning good profits. A probable reason could be the statutory nature of the services. Nevertheless, this study recommends improving the quality of services and differentiating services between age groups for further improvement.
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Financial sustainability management of the insurance company: case of Ukraine
Ruslana Pikus
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Nataliia Prykaziuk
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Mariia Balytska
doi: http://dx.doi.org/10.21511/imfi.15(4).2018.18
Investment Management and Financial Innovations Volume 15, 2018 Issue #4 pp. 219-228 Views: 5195 Downloads: 815 TO CITE АНОТАЦІЯIn the current conditions of the Ukrainian economy, which is characterized by crisis phenomena and frequent changes in legislation, the insurance organizations are facing a number of difficulties in maintaining their financial sustainability. Moreover, these processes take place under the increased requirements for solvency of insurers. However, a significant part of domestic insurance companies is financially unstable, which is conditioned not only by the lack of funds, but also by the low level of management. This situation hinders the further development of the insurance market in Ukraine and has a negative impact on all areas of the domestic financial system and prevents it from successful integration into the European financial field. In order to address this problem, it is necessary to distinguish the key groups of risks that affect the financial sustainability of insurance organizations, among which there are the following: insurance, strategic, market risk, risk of inefficient capital structure, risk of limiting the insurance company’s liquidity, tax risk, investment risk, operational risk, the risk of ineffective organizational structure of the enterprise, and information risk. It should be noted that under conditions of changing environment, the impact of these risks only increases, and therefore the task of minimizing the impact of these risks on the activities of insurance companies is highly important. Accordingly, the authors of the article proposed a four-stage strategy to manage the financial sustainability of the insurance company, the purpose of which is to identify the risks of limiting the insurer’s financial sustainability, their qualitative and quantitative assessment, as well as the development and implementation of appropriate measures to minimize and eliminate unacceptable consequences.
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Analyzing firm-specific factors affecting the financial performance of insurance companies in South Africa
Insurance Markets and Companies Volume 14, 2023 Issue #1 pp. 8-21 Views: 3819 Downloads: 938 TO CITE АНОТАЦІЯThis study aims to investigate the effect that firm-specific factors have on the financial performance of South African insurance companies. This paper looked at the performance of 36 insurers that are publicly traded and have quantifiable markets from 2008 to 2019. The return on assets (ROA) was calculated as a function of the financial performance in this study. While the firm size, leverage ratio, premium growth rate, liquidity ratio, and tangibility of assets were examined as dependent factors using the panel data regression technique, the premium growth rate, liquidity ratio, and tangibility of assets were explored as independent variables. According to the findings of the regression analysis, other firm-specific factors, with the exception of leverage and liquidity ratios, do not have a statistically significant influence on the financial performance of South African insurance companies. A negative and insignificant association was discovered between premium growth rate and ROA at –0.0023 and tangibility of assets and ROA at –0.0113. There was a strong positive and significant relationship between liquidity ratio and ROA at 0.0927, while the size had a positive but insignificant relationship with ROA at 0.0039. Leverage ratio and ROA had a negative but significant relationship at –0.1512. This study suggests that the use of automated systems and insured techs will be advantageous in cutting costs associated with policyholder enrollment, claims agreement, and even easily achieved tailor-made policy initiatives.

