Reinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability

Abstract

Context: insurance companies are important to society, since they guarantee financial protection to individuals from property losses, in addition to fostering the capital market through the allocation of guarantee assets. Thus, it is essential to evaluate the instruments that guarantee their long-term financial solvency. Among them are the adoption of reinsurance treaties, the sizing of the solvency capital, and the actuarial modeling of risk processes, which allow the measurement of the ruin probability. Objective: estimate the ruin probability in risk processes with the adoption of reinsurance contracts (quota share and excess of loss), compared to scenarios without such treaties. Methods: the Cramér-Lundberg process was simulated using the Monte Carlo method, adjusting several probabilistic distributions to the severity of the compound Poisson process, which is calibrated with a set of 3,917,863 real microdata, from 30 insurance lines of business. Results: it was found that, although each branch presents particularities in the claim severity, the correct choice of reinsurance (proportional or not) implies the reduction of the ruin probability for a fixed solvency capital. Conclusion: the appropriate choice of the reinsurance contract, especially when there is evidence of high kurtosis in the claim values, intensifies the exponential decline in the relationship between the solvency capital and the ruin probability.

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“…These requirements are derived from international agreements known as "Basel III" for financial institutions (Andrieş et al, 2022;Oliveira & Ferreira, 2019) and "Solvency II" for insurance companies (Carvalho & Cardoso, 2021;Chen & Yuan, 2017;Macohon et al, 2017). In essence, regulations based on these agreements require institutions to assess their risks and, based on this, to maintain a minimum amount of capital to minimize the risk of insolvency (Euphasio Junior & Carvalho, 2022;Gupta & Liang, 2005;Ramsden & Papaioannou, 2019).…”

“…In Brazil, for example, banks must follow the determinations of the Central Bank, which are based on the "Basel III" pillars (Oliveira & Ferreira, 2019). Insurers, on the other hand, must follow the rules of the Superintendence of Private Insurance (Susep), which establishes the minimum required capital, i.e., the minimum amount of capital that insurers must maintain in order to operate (Carvalho & Cardoso, 2021;Euphasio Junior & Carvalho, 2022;Macohon et al, 2017).…”

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“…Mais apropriadamente sob a égide social, os seguros cumprem distintas funções, dentre as quais se destacam: (a) a manutenção patrimonial dos indivíduos por meio dos produtos vinculados a coberturas de danos (Euphasio Junior & Carvalho, 2022); (b) o acúmulo de poupança visando a financiar os pagamentos de aposentadorias e pensões, seja na esfera da previdência social (Afonso & Carvalho, 2021), seja na previdência complementar; e (c) o amplo acesso à rede privada de hospitais por meio de planos e seguros de saúde (Areias & Carvalho, 2021). Em suma, trata-se de um setor inteiramente voltado ao oferecimento de garantias essenciais para que as nações possam se desenvolver de forma próspera.…”

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“…No Brasil, por exemplo, os bancos devem seguir as determinações do Banco Central, que se baseiam nos pilares da "Basileia III" (Oliveira & Ferreira, 2019). Já as seguradoras devem cumprir as regras da Superintendência de Seguros Privados (Susep), que estabelece o capital mínimo requerido, i.e., o valor mínimo de capital que a seguradora deve manter para operar (Carvalho & Cardoso, 2021;Euphasio Junior & Carvalho, 2022;Macohon et al, 2017).…”