Challenges of Islamic Insurance

The aim of this paper is to study the stability of insurance companies. The majority of works on this topic has focused on the determinants of financial stability. Therefore, they interested in the Z-score, focused on the ROA, as well as the panel method. Unlike previous work, we have formed a score made up of indicators of efficiency, effectiveness, profitability, solvency, productivity, investment and risk, as well as macroeconomic indicators. Our sample consists of 30 insurance companies, 15 of which are shariaa compatible. The choice of these companies is justified by their contribution to the total assets of the both types of finance. This selection method allowed us to have a global idea on the effectiveness, efficiency, risk and stability of the two insurance sectors. The analysis of the stability scores, determined using the scoring and logit transformation method, revealed that Islamic insurance companies are more stable than conventional insurance companies. From a risk perspective, Islamic insurance companies are less risky than conventional insurance companies. They lose, on average, 1.598% of their assets against 3.704% for conventional insurance companies. This observation related to three types of risk, namely; liquidity risk, market risk and credit risk. Furthermore, this empirical investigation revealed that takaful companies are not immune to the toxic funds of the crisis. Likewise, we note that Islamic insurance companies are sensitive to political shocks such as that of the Arab revolutions that took place in 2011.


INTRODUCTION
A takaful contract is a collective donation contract under which a natural or legal person pays a sum not previously defined to the partners' account, which differs from that of the shareholders. These two accounts are managed and invested separately by the takaful company in return for a share of the profits. Similarly, a takaful contract is a contract through which the transfer of a person's losses is made to a committee account. Thus, if the result is positive, the takaful company is expected to distribute the profit among the members. On the other hand, if the members' account is in deficit it must cover these losses. To do this, it uses technical reserves, a request for donation by members or even by means of a "qarth hasan" from a re-takaful company or the shareholders' account. This loan, "qarth hasan," will be reimbursed later by future earnings.
The second section is devoted to the description of the data, the variables and the methodology used. Finally, in the third section, we will present and discuss the main results obtained.

REVIEW OF THE LITERATURE
Nowadays, the topic of stability is of major interest. Although it is quite important for the insurance sector than the banking sector, studies are rare. Das et al. (2003) indicated that the failure of insurance companies could lead to major and costly disruptions. Furthermore, Cummins et al. (2017) suggested that the insurer's solvency not only protects the insured by ensuring that the insurer will be able to meet its financial obligations in the future, but also contributes to the stability of the financial system.
Indeed, financial stability can be defined as a specificity of the financial system, intended to cope with systemic shocks in a sustainable manner and without generating major disruption. It is used to efficiently allocate the financial resources within the economic department and to identify and manage risks effectively (Mirela, 2008). However, insurance companies are faced with two types of risks, namely specific risks and nonspecific risks. Non-specific risks mainly consist of liquidity risk, market risk, insolvency risk and operational risk. On the other hand, the specific risk is an intrinsic risk, linked to the activity of insurance companies, for example the underwriting risk (Krenn and Oschischnig, 2003). In this regard, Mirela (2008) attempted to develop a mathematical model allowing insurance companies to control their level of stability and avoid the risk of insolvency and therefore bankruptcy. This model is based on optimizing the subscription portfolio and supports the creation of an adequate insurance fund to cover compensation and the risk of insolvency. However, this model is only applicable if the conditions of competition are ensured. Mathematically speaking, the level of financial stability is an increasing function of the variation in the net premium rate and the number of areas insured. As a result, the insurance company can improve its level of stability by increasing the net premiums or the number of areas insured. However, to reduce the risk, it must cede part of its contracts to the reinsurance company.
Moreover, Tomislava et al. (2019) were interested in determining internal and external financial stability of insurance companies in Central and Eastern Europe. The results of this study revealed that the stability of Croatian insurers is positively influenced by the size of the insurer. In Hungary and Poland, on the other hand, reinsurance is an important factor positively affecting soundness. In fact, these results are consistent with those of Cummins et al. (2008) andBerger et al. (1992). Cummins et al. (2008) indicated that the reinsurance reduces the risk of insolvency by stabilizing losses, limiting specific risks and increasing protection against disasters. Similarly, Berger et al. (1992) stated that the reinsurance is an important risk diversification mechanism in insurance markets, as it protects the insurer against catastrophic loss and possible insolvency.
Zarina et al. (2018) focused on Solvency II and the internal factors of business stability. The results of this paper shows that non-life insurance companies in the Baltic were highly capitalized in 2016, with a total capital surplus of 237 EURO million. In addition, the analysis of the solvency ratios, the risk profile and the excess capital suggests that the Baltic non-life insurance market is more stable than that of Europe and that there is strong growth potential. However, Baltic insurance companies need to lower their associated risk level.
In the same wake, Ziemele and Voronova (2013) studied the solvency as a tool for achieving financial stability in the insurance industry. This paper examines the role of Solvency II in improving the financial stability of insurance companies. The analysis of the new solvency system shows that the Solvency II system will reveal the true financial situation of insurers and improve transparency and confidence throughout the sector. The introduction of riskbased regulatory requirements will ensure that a fair balance is struck between strong protection for policyholders and reasonable costs for insurers. Cummins et al. (2017) explored the relationship between the stability of life insurance companies and competition. To do this, Cummins et al. (2017) used the z-score, based on the ROA, and Boone's indicator as a proxy reflecting the level of competition. This analysis covers the period 1999-2011 and covers a sample of 10 EU countries, namely, Austria, Belgium, Denmark, France, Germany, Italy, Netherlands, Spain, Sweden and the United Kingdom. The main conclusion of this paper is that competition has a positive impact on the financial stability of insurance companies. Pasiouras et al. (2013) studied the relationship between insurer stability and insurance regulatory policies. They used an international dataset of more than 1700 insurers from 46 countries. The regulatory variables used consist of the capital requirement index, the supervisory power index, the technical provisions index and the investment index. Likewise, they used governance indices such as the internal control index, the corporate governance index and the supervisory power index. The results of this investigation suggest that the supervisory powers of the competent authorities, as well as the regulations relating to technical provisions and investments, appear to have a positive impact on stability. Schich (2009) examined the role of non-life insurance and investment portfolios in the instability of the insurance industry. It states that the main sources of destabilization of the insurance system are mortgage insurance and financial guarantee companies. A number of exposures to credit and market risks have been revealed, notably in mortgage insurance and financial guarantee activities. Chen et al. (2004) studied the determinants of financial stability in Asian countries. They were mainly interested in Japan, Malaysia, Taiwan and Singapore. The results of this study suggest that firm size, investment performance, liquidity ratio, excess growth and operating margin are the determinants of stability for non-life insurance companies. On the other hand, the stability of life insurance companies is sensitive to the size of the company, the composition of the assets and the performance of investments.
From a critical point of view, the works exposed previously in the literature review focused on the study of the determinants of financial stability. To do this, the authors interested in the Z-score, focused on the ROA, as well as the panel method. In addition, comparative studies between conventional and Islamic insurance companies have not addressed this subject. Thus, this work could be a starting point for further research.

METHODOLOGY
The aim of this paper is to study the stability of Islamic and conventional insurance companies. Unlike previous work, we calculated the efficiency and effectiveness scores, using the SFA and DEA method, instead of using ratios reflecting these two indicators. Then, the efficiency and effectiveness scores were used together with the profitability, solvency, productivity, investment and risk indicators, as well as macroeconomic indicators in order to calculate the stability scores of the two types of insurance company (Islamic and conventional).
Efficiency 1 is the rational use of available resources to achieve pre-set objectives, it is the ability to achieve the objectives and goals envisaged while minimizing the resources committed.
On the other hand, effectiveness measures the achievement of objectives without any measure or precision of the resources employed.
In order to study these two indicators, we will use the DEA method and the SFA method.
Our sample consists of 30 insurance companies, 15 of which are Islamic.
These companies were selected based on their respective contributions in the total assets of the Islamic and conventional insurance sector and the availability of their financial losses. The insurance companies are distributed as follows in Table 1.

Data Envelopment Analysis
The nonparametric method was developed by Farrell (1957) in his paper "The measurement of productive efficiency." Farrell (1957) was interested in the phenomenon of decision-making and was based on the choice of different baskets (Input; Output) available, and which maximize profits. This method was modified by Charnes, Cooper and Rhodes (1978) who relied on the data enveloping of decision units (Drake, L., Maximilian, H.J.B., Simper, R. 2006), hence the name Data Envelopment Analysis (DEA).
If we have several inputs and outputs, the score will be presented as follows (Srinivas Talluri, 2000): Lesdefinitions.fr : online dictionary.
weighted sum of outputs Effectiveness weighted sum of inputs = To judge the efficiency of a basket (input; output) and determine its efficiency score, knowing that there are n decisions, m inputs and outputs, we can use the following form of the DEA model (Srinivas Talluri, 2000): Where: k=1….s, J=1….m, I=1….n X ji = Input price used by i DMU. Y ki = Price of k output produced by i DMU. V k = Weighting attributed to the outputs. U j = Weighting attributed to inputs.
However, as presented by Charles et al. (1978), equation (2) can be written as follows: The DEA allows determining the maximum of inputs to be injected into a production mechanism above which the benefit drops.
To estimate the efficiency scores of the DMUs we used the following variables in Table 2.

Stochastic Frontier Analysis
The cost function is presented by Aigner, Lovell and Schmidt (1977) and Meeusen and Van Den Broeck (1977) in the following form: Ln TC= f (y i , p k ) + ε Where: TC = Operating cost. y i = Outputs vector.
However, any inefficient DMU, from income point of view, must reduce its marginal cost per unit produced. This relation can be written in the following form (Laurent, 2010): The translog profit function is more important than the translog cost function because it explains the input-output relationship.
The profit-efficiency function was presented by Isik and Hassan (2002) in the following form (Ihsan, I. 2002): Since the profit can be negative, we must add a constant "a" so that (π + a) is positive. This constant is usually greater than the maximum loss.
To estimate the efficiency scores of the DMUs, we used the following variables in Table 3.

Scoring Method
The third empirical investigation in our paper focuses on the stability of the two types of insurance companies, and their respective z-scores can be written as follows: Then, we will use the exponential transformation of the logit model to derive the respective stability levels of insurance companies (Table 4). This probabilistic relation can be expressed as follows:

Estimation of the Variables
The descriptive statistics of the different variables showed that conventional insurance companies were 7 times more productive than takaful companies Table 5 and 6). This productivity gap is due to the size of their customer portfolio and product portfolio. In   addition, conventional insurance companies are characterized by their large size. In fact, these two tables illustrate that conventional insurance companies admit an average cost of $ 278.3190 million against $ 153.6636 million for Islamic insurance companies and they are 13 times more profitable than takaful companies. These results confirm the role of the liberalization of the insurance sector that has mobilized resources to this sector, improve and diversify its products and services.
The results of estimates, made using the OLS method, show that the R squares of the translog cost function is 0.863626 for conventional insurance companies and 0.956536 for takaful       (Table 7). With regard to translog profit-function, 92.99% and 74.77% of the data variability of conventional insurance companies and takaful companies are respectively around the average. In order to verify these results, we performed the Fisher test. The results of this test suggest the rejection of the null hypothesis which states that the explanatory variables "σ1" are equal to those non-explanatory "σ2" such that: -H0 : σ 1 ² = σ 2 ² -H1 : σ 1 ² ≠ σ 2 ² The homogeneity test revealed that the explanatory variables are 46 and 96 times more than the non-explanatory variables in the LC and LR function of conventional insurance companies and 158 and 21 times, respectively, for takaful companies.
Thus, we can conclude that the model is globally significant.

Insurance Companies
In this section, we will present the empirical results of the study of the cost and profit x-efficiency of both types of insurance companies.
Based on Tables 8 and 9 we note that conventional insurance companies are more cost-effective than takaful companies. The most effective insurance companies are Allianz and PT Ansuransi Adira Dinamika, which have respective cost effectiveness scores of 84.12% and 80.87%. These scores were calculated over an 11-year period from 2004 to 2014. Over this period, the scores vary between 78.98% and 84.12% for conventional insurance companies and between 74.32% and 80.87% for takaful companies. Before the crisis, both scores were growing at a faster pace because of the competition that gave rise to new cost-saving potentials (Paul et al., 2008). In view of the work of Paul et al. (2008), Germany and France are the two countries most affected by mergers and acquisitions and they have average scores of 0.985 and 0.988 respectively. In the same vein (cross-country study), Anoop (1996) concluded that: • The average score of x-inefficiency is 0.27.
• Insurance companies in the United Kingdom and Switzerland have a high degree of inefficiency compared to those in France and Finland. However, Awang and Aleng (2012) concluded that the insurance sector in Malaysia improved between 2007 and 2009 and that a 1%  Ha: mean(diff) < 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Ha: mean(diff) > 0 Pr(T > t) = 1.0000 cost reduction will improve the efficiency of Malaysian insurance companies by 92%.
In summary, cost efficiency scores range from 0.7 to 0.99 with a dominance of traditional insurance companies and mutual societies. In contrast, takaful firms are more efficient in terms of profit (Awang and Aleng, 2012) and their scores vary in the literature between 0.806 and 0.957. On our part, the review of the "profit efficiency" of Islamic and conventional insurance companies resulted in an average score of 83.53% and 87.85% in favor of takaful companies as shown in the Table 10 and 11.
Despite their protectionist structure, Islamic insurance companies, as conventional insurance companies, were affected by the creditsubprime. After the tornado and precisely in 2010 the level of profit-efficiency of takaful companies has improved except the Arab revolution period. The Arab spring has negatively affected the production of insurance resulting in lower scores of "profitefficiency".

Efficiency of Islamic and Conventional Insurance Companies
The DEA method allows studying several types of efficiency namely CRS, VRS, SCALE Efficiency ...ect. In the present work, we have limited ourselves to the study of the VRS because it takes into account the variability of inputs and outputs over time. This study resulted in the following scores (Table 12).
From Tables 12 and 13, we note that despite the drop in their efficiency levels, insurance companies were able to be efficient between 2008 and 2010. Their scores have steadily increased until 2011 and 2012 during which time they were impacted by the Arab revolutions. In fact, Takaful International, PT Ansuransi Adira Dinamika and PT Reasuransi Nasional Indonesia are the only takaful companies that have not been affected by the reduction of production and cost growth in the time of the uprisings. The other takaful company that has been able to withstand this outbreak is Best Retakaful which has had a score drop of 0.002 during the crisis. With regard to conventional insurance companies, the Arab revolutions have no impact, but more than 73% of our sample experienced lower levels of efficiency in the crisis period. Rahman (2013) concluded that Bangladeshis takaful companies are less profitable (by 9%) and perform better than conventional insurance companies. The takaful companies' score in this study is 0.974. Similarly, in Pakistan and Malaysia, takaful companies are more efficient than traditional insurance companies ( On the other hand, Mansor and Radam (2000), Norma and Nur (2011) and Norma (2012) concluded that traditional insurance companies dominated takaful firms, with a score of 0.773 (Norma, 2012) between 2007 and 2009, a score of 0.794 (Norma and Nur, 2011) between 2000 and 2005 and 0.7265 (Mansor and Radam, 2000) between 1988 and 1998.    The study conducted by Norashi Kim et al. (2011), using VRS, resulted in an average efficiency score of 0.703. In addition, Norashi Kim et al. (2011) suggest that takaful companies in GCC countries admit a score that varies between 53% and unity against a score that does not exceed 65% in Malaysia (Miniaoui and Chaibi, 2014).
The Yang (2006) study resulted in a score of 74.04% for Canadian insurance companies. This score is the average of the productivity level (76%) and the inverse of the investment efficiency score (52%). According to the work Yang (2006), Liang et al. (2007) found that Canadian life and health insurance companies had scores of 0.79 and 0.83, with an average score of 0.81.

Stability of Islamic and Conventional Insurance Companies
As illustrated above, conventional insurance companies are more efficient than takaful companies. In contrast, takaful companies are more effective. However, we note in Tables 14 and 15 that takaful companies admit minimal losses compared to traditional insurance companies. Although conventional insurance companies are more profitable, they invest less than Shria-compatible ones. In fact, takaful companies invest on average 26.33% of their assets against an investment rate of 8.14% for their conventional counterparts. On the other hand, conventional insurance companies have an average cost to income ratio of 86.4% compared to 5.118% for takaful companies and a solvency ratio of 11.69 against 2.98% for Islamic insurance companies. This shows that conventional insurance companies are more productive and solvent than Islamic insurance companies.
In view of the stability scores shown in Table 16 and 17, we note that Islamic insurance companies are more stable than conventional insurance companies. The takaful companies admit an average stability score of 93.3030% against 79.6763% for conventional insurance companies. The most stable takaful company is B.E.S.T Retakaful with a score of 99.622% while the least stable is PT Asuransi Jiwa Asih GreatEastern with a score of 54.3123%. On the other hand, the most stable conventional insurance company is Munich Re, while the least stable is Allianz and they admit stability scores of 95.473% and 57.641% respectively.
From a risk perspective, Islamic insurance companies are less risky than conventional insurance companies. They lose on average 1.598% of their assets against 3.704% for conventional insurance companies. This observation relates to three types of risk namely, liquidity risk, market risk and credit risk. From the point of view of liquidity risk and credit risk, takaful companies lose, respectively and on average, 0.697% and 0.5784% of their assets against 0.205% and 0.233% for conventional insurance companies. On the other hand, Islamic insurance companies lose 9.88% less than conventional insurance companies in terms of market risk. This seems logical because traditional insurance companies are more active in financial markets than Islamic insurance companies that tend to invest in real estate. They invest mainly 26.327% in real estate, energy, industrial and new technologies. Their losses in terms of stability did not exceed 0.3% (0.2465% for conventional insurance and 0.1155% for Islamic insurances), which once again testifies to the robustness of Islamic financial institutions during the crisis. Similarly, we note that Islamic insurance companies are sensitive to political shocks such as that of the Arab revolutions that took place in 2011. These revolutions have lost to Islamic insurance companies 0.22% of their stability scores. This observation seems entirely logical because of the nature of takaful products marketed on the insurance market. As a result, takaful companies are expected to commercialize new products in order to diversify their product portfolio, reduce the associated risk and thus improve their profitability and productivity.
Similarly, Waheed and Saad (2017) and Waheed and Saad (2017) revealed that takaful insurance is more resilient in times of crisis.
Indeed, Waheed and Saad (2017) compared the demand for Islamic insurance with that of conventional insurance in 14 countries during the period 2005-2014. Empirical results suggest that demand for Islamic and conventional insurance is negatively affected by GDP per capita. Similarly, the savings rate has a negative impact on the demand for conventional insurance since conventional savings products are replacing conventional insurance. However, the increase in average income is positively (negatively) related to demand for Islamic insurance in the Middle East (ASIA), which is likely related to different Islamic finance practices in both regions.
In the same spinning, Waheed and Saad (2017) focused on the analysis and differentiation of the determinants of conventional and Islamic insurance in the regions of Asia and the Middle East. They applied fixed and random effects regression models to assess the impact of macroeconomic and demographic factors on conventional and Islamic insurance. The estimation results suggest that takaful companies are more stable than conventional insurance companies. In addition, the net income and financial sector variables have a positive and significant impact on insurance demand in all regions. Thus, the development of the financial sector is a significant determinant of demand for insurance and Takaful in the Asian region. For the Middle East region, the development of the financial sector affects only the demand for conventional insurance.