Sensitivity of the Stability Bound for Ruin Probabilities to Claim Distributions

Bareche, Aicha; Cherfaoui, Mouloud

doi:10.1007/s11009-018-9675-7

“…Proposition 2.1 and Theorem 2.2 below give upper bounds for d(p τ , p τ ). The relevant results on stability (continuity) of the infinite horizon ruin probability can be found, for instance, in [13,17] for the Cramer-Lundberg risk process, and for more general risk model in [2,3,9,10]. On the other hand, we are not aware of any continuity inequalities for densities of ruin time.…”

Section: Theorem 22 and The Results Of Section 3 Imply That Under Somentioning

confidence: 99%

Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes

Gordienko

¹

,

Chávez

²

,

Vázquez-Ortega

³

2021

Appl. Math. (Warsaw)

1

0

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“…This methodological option is a simplifying hypothesis, which could generate some bias in the estimates. Despite the fact that the average duration of the 3,917,863 policies is 327 days (with a standard deviation of 110 days), this problem does not compromise the estimates obtained by MCM on annual basis, which, as argued throughout the paper, are strongly stable (Bareche & Cherfaoui, 2019;Gatto, 2020), mitigating eventual problems of this nature. Furthermore, as the process simulation is based on collective risk modeling, the individual policies effect is diluted in the line of business' standard set.…”

Section: The Databasementioning

confidence: 93%

“…The main one is the approach via the Monte Carlo method (MCM), a stochastic simulation that provides an empirical approach to the ruin probability calculation. More recently, Touazi, Benouaret, Aissani and Adjabi (2017) -using a non-parametric approach -, Bareche and Cherfaoui (2019) and Gatto (2020)both using heavy-tail distributions -demonstrated that the estimates obtained by the simulation methods are strongly stable.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Reinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability

Euphasio

¹

,

Carvalho

²

2022

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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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“…Esta opção metodológica é uma hipótese simplificadora, que poderia gerar algum viés nas estimativas. Entretanto, como o tempo médio de duração das 3.917.863 apólices da base é de 327 dias (com desvio padrão de 110 dias), este problema não compromete as estimativas obtidas por MMC em bases anuais, que, como argumentado ao longo do texto, são fortemente estáveis (Bareche & Cherfaoui, 2019;Gatto, 2020), mitigando eventuais problemas desta natureza. Ademais, como a simulação do processo baseiase em modelagem de risco coletivo, o efeito de apólices individuais está diluído no conjunto padrão do ramo.…”

Section: A Base De Dadosunclassified

Resseguro e Capital de Solvência: Atenuantes da Probabilidade de Ruína de Seguradoras

Euphasio

¹

,

Carvalho

²

2022

Rev. adm. contemp.

2

0

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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.

show abstract

Sensitivity of the Stability Bound for Ruin Probabilities to Claim Distributions

Cited by 7 publications

References 23 publications

Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes

Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes

Reinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability

Resseguro e Capital de Solvência: Atenuantes da Probabilidade de Ruína de Seguradoras

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