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.

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

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.

Modeling the Future Value Distribution of a Life Insurance Portfolio

This paper addresses the problem of approximating the future value distribution of a large and heterogeneous life insurance portfolio which would play a relevant role, for instance, for solvency capital requirement valuations. Based on a metamodel, we first select a subset of representative policies in the portfolio. Then, by using Monte Carlo simulations, we obtain a rough estimate of the policies’ values at the chosen future date and finally we approximate the distribution of a single policy and of the entire portfolio by means of two different approaches, the ordinary least-squares method and a regression method based on the class of generalized beta distribution of the second kind. Extensive numerical experiments are provided to assess the performance of the proposed models.

TEST FOR CHANGES IN THE MODELED SOLVENCY CAPITAL REQUIREMENT OF AN INTERNAL RISK MODEL

ABSTRACT In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

Pandemic Crisis: Malaysian Takāful Market

With the progressive number of COVID-19 cases, this pandemic has adversely impacted the Takāful market in different forms containing liquidity impact, financial market volatility and solvency capital. This study describes the Malaysian takāful and insurance market throughout the COVID-19 crisis as well as its response to alleviate the burden faced by policyholders/ certificate holders of life insurance and family takāful plans from the economic and Sharīʽah point of views. Qualitative approach is applied in this study to collect information, documents and data accordingly concerning to the topic discussed. The data will be explored using qualitative content, narrative, and discourse analysis to deliver its results and discussion. By understanding the precarious scenario of the Malaysian takāful and insurance market during the COVID-19 pandemic, we can further enhance the support to the regulator who has taken the initiative to direct the insurance and takāful industry to initiate adequate response to facilitate policyholders/ certificate holders during the outbreaks and decide what the best way forward would be as aligned with Maqāṣid al-Sharīʽah. This will ensure its positive impact in the Takāful market, not only to nurture sustainability in our ecosystem, stabilize the socio-economic but to safeguard policyholders/certificate holders accordingly so they could withstand pre, present and post pernicious outbreaks and pandemics. This study inspires Takāful practitioners, policyholders/ certificate holders, academicians, and the society to recognise the importance of takaful industry and it’s preventive measures to avoid takāful loss in this swift spread of COVID-19 comprising catastrophic reserves by takāful operators to mitigate adverse catastrophic risks to human life, and building a more humanising takāful which is in tandem with Maqāṣid al-Sharīʽah that attracts more potential policyholders/ certificate holders.

Fire Risk Sub-Module Assessment under Solvency II. Calculating the Highest Risk Exposure

The European Directive 2009/138 of Solvency II requires adopting a new approach based on risk, applying a standard formula as a market proxy in which the risk profile of insurers is fundamental. This study focuses on the fire risk sub-module, framed within the man-made catastrophe risk module, for which the regulations require the calculation of the highest concentration of risks that make up the portfolio of an insurance company within a radius of 200 m. However, the regulations do not indicate a specific methodology. This study proposes a procedure consisting of calculating the cluster with the highest risk and identifying this on a map. The results can be applied immediately by any insurance company, covered under the Solvency II regulations, to determine their maximum exposure to the catastrophic man-made risk of fire, instantly providing them with the necessary input for calibration of the solvency capital requirement.

Approaching of Financial Ratio Analysis of Canara Bank and ICICI Bank

A ratio is defined as ‘the indicated quotient of two mathematical expressions’ and as ‘the relationship between two quantitative terms between figures which have a cause and effect relationship or which are connected with each other in some manner or the other. The sources of primary data are survey, observation and experimentation and secondary data collected through various websites. A noticeable point is that a ratio reflecting a quantitative relationship helps to perform a qualitative judgment; such is the nature of all financial ratios “Ratio can assist management in its basic functions of forecasting, planning coordination, control and communication”. It is helpful to know about the liquidity, solvency, capital structure and profitability of an organization. It is helpful tool to aid in applying judgment, otherwise complex situations.