Discrete Time Ruin Probability for Takaful (Islamic Insurance) with Investment and Qard-Hasan (Benevolent Loan) Activities
Round 1
Reviewer 1 Report
Major comments
In my opinion, this study focuses on a topic that is too narrow to attract attention. The introduction should be polished by more general descriptions. (Most of the details on Takaful needs to be put in section 2.2.)
In the introduction section, the authors need to emphasize why the Takaful instrument deserve to be analyzed and what the analysis can contribute.
I like the authors' effort to introduce readers to an Islamic insurance, "Takaful." In my understanding, this financial instrument seems to be related with socially responsible investment (SRI) issue, a recent interest of finance guys. The authors can review more references regarding this issues and relate their study to the SRI issue so that they can attract general attention.
Minor comments.
The authors should correct grammar errors or typos in their manuscript.
For example,
In the abstract
We also find that our proposed Takaful model has a better performance compare to the conventional counterpart in terms of the probability of ruin.
on line 62, Upper cases are not necessary for Enterprise Risk Management.
Author Response
Thank you for the insightful comments and suggestions on our manuscript. Here are some points (in italic) to answer Reviewer 1's comment:
Major comments
- In my opinion, this study focuses on a topic that is too narrow to attract attention. The introduction should be polished by more general descriptions. (Most of the details on Takaful needs to be put in section 2.2.)
While the Takaful market is rather small globally, but as pointed out in the introduction that its importance will grow with time. In fact as mentioned by IFDR (2018) that the Takaful industry is still growing at the rate of 19% in 2018, with total assets USD 46 billion from 324 Takaful operators in 47 countries. We have moved some details about Takaful insurance to Section 2.2.
- In the introduction section, the authors need to emphasize why the Takaful instrument deserve to be analyzed and what the analysis can contribute.
In the introduction section, in particular on page 2, in line 78, we mention that our study contributes to the development of Takaful risk models. With the growing importance of the market for Takaful, we believe that it will be extremely to consider some quantitative techniques in analyzing Takaful, especially the existing research along this line of inquiry is extremely limited. Hence our proposed model and analysis can provide constructive insights to foster the development of Takaful
In particular, on page 3, line 102, we have also added a remark indicating that results of our numerical study provide important insight into the optimal structure of the proposed Takaful model. In particular, our results demonstrate that by providing qard-hasan facility, the Takaful product outperforms the conventional counterpart in terms of the lower probability of ruin. We have also found that if the operator invests the undrawn-down qard-hasan fund, then following the Shariah rule to pay off the qard-hasan undertaking may produce better performance.
- I like the authors' effort to introduce readers to an Islamic insurance, "Takaful." In my understanding, this financial instrument seems to be related with socially responsible investment (SRI) issue, a recent interest of finance guys. The authors can review more references regarding this issues and relate their study to the SRI issue so that they can attract general attention.
We have added a paragraph on page 1, between lines 19 to 32, that explains the growing trend of seeing Islamic finance and Takaful products as a subclass of SRI. Even though Takaful products follow a major religion (Islam) rule, these products have attracted attention of a broader community, including the non-muslim community.
Minor comments.
The authors should correct grammar errors or typos in their manuscript.
For example,
In the abstract
We also find that our proposed Takaful model has a better performance compare to the conventional counterpart in terms of the probability of ruin.
on line 62, Upper cases are not necessary for Enterprise Risk Management.
We have proofread our manuscript and several grammatical errors have been corrected.
Reviewer 2 Report
This is a timely and original study that proposes a framework of Hybrid-Takaful that incorporates investment activities and qard-hasan facility. The authors find that the qard-hasan facility improves performance of the fund as it decreases the finite-time ruin probabilities. The following recommendations aim at the further improvement of the study;
- The authors are recommended to bring a further justification on why discrete-time models often turn out to be more realistic.
- On Page 4 of 23, please correct the "qrd-hasan"
- The authors need to clarify the underlying reason that in their model
the borrower will repay the loan only if they generate a positive surplus in the future. - A brief definition of "undrawn-down loan" will be useful.
- On Page 7 of 23, what is "iid"?
- On Page 17 of 23, please correct "this result can be explain by the fact" as "this result can be explained by the fact".
- The authors need to bring further explanations on how paying off the qard-hasan undertaking not only follows the Shariah rule
Author Response
The authors would like to thank the insightful comments from Reviewer 2. Please kindly find some points to answer comments from Reviewer 2 (in Italic):
This is a timely and original study that proposes a framework of Hybrid-Takaful that incorporates investment activities and qard-hasan facility. The authors find that the qard-hasan facility improves performance of the fund as it decreases the finite-time ruin probabilities. The following recommendations aim at the further improvement of the study;
- The authors are recommended to bring a further justification on why discrete-time models often turn out to be more realistic.
We have added an explanation on page 4, line 124, stating that in reality insurance claims occur in discrete time. For example, for automobile insurance, the claim dataset is usually presented monthly. Hence, for investigation of insurance problems, discrete-time models often turn out to be more realistic.
- On Page 4 of 23, please correct the "qrd-hasan"
This has been corrected.
3. The authors need to clarify the underlying reason that in their model
the borrower will repay the loan only if they generate a positive surplus in the future.
On page 6, line 215, we have added an explanation that our assumption on qard-hasan features follow the IFSB’s rule. This fact has also been explained in Section 2.2.
- A brief definition of "undrawn-down loan" will be useful.
On page 6, line 219, we have added an explanation that the undrawn-down loan is the loan facility that is still available in the external fund account.
5. On Page 7 of 23, what is "iid"?
On page 8, line 290, we have explained the abbreviation “iid” as “independent, identically distributed” random variable.
6. On Page 17 of 23, please correct "this result can be explain by the fact" as "this result can be explained by the fact".
It has been corrected.
7. The authors need to bring further explanations on how paying off the qard-hasan undertaking not only follows the Shariah rule
We are not sure with the above comment, as it seems the sentence is not complete. But, we try to understand the comment as follow : “The authors need to bring further explanations on how paying off the qard-hasan undertaking not only follows the Shariah rule but also has a positive effect on the business, if we invest the undrawn-down qard-hasan.” We have added the conclusion with “in the non risky asset” on page 20 line 470 to clarify our simulation and finding.
We have also added an explanation on page 20 line 470 “By paying off the loan undertaking to qard-hasan fund, we can guarantee that the money will grow at the corresponding rate of return. If the money remains in the surplus fund, then the investment return is delayed until the surplus fund reaches the investment trigger level.”
Round 2
Reviewer 1 Report
The authors in the current version of manuscript have emphasized why the Takaful insurance is worth being studied. Also they are clarifying their contribution. It seems that the authors have polished their manuscript well.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Major comments
In my opinion, this study focuses on a topic that is too narrow to attract attention.
I like the authors' effort to introduce readers to an Islamic insurance, "Takaful." In my understanding, this financial instrument seems to be related with socially responsible investment (SRI) issue, a recent interest of finance guys. The authors can review more references regarding this issues and relate their study to the SRI issue so that they can attract general attention. (In the current version, review of literature lacks.)
In the modeling part, the authors used the concept of first-passage time. In finance literature, closed-form solutions of first-passage time have been studied in depth. The authors should review and try to apply this method to theirs.
Also, in my view, the authors depend too much heavily on Kim and Drekic (2016)'s modelling, which makes me finding the contribution of this study very marginal.
Minor comments.
on line 218, pmf should be rephrased by probability mass function. More importantly, the sentences around this line repeat those of Kim and Drekic (2016) and must be paraphrased.
The authors should correct grammar errors or typos in their manuscript.
For example,
on line 10-11,
We also find that our proposed Takaful model has a better performance compare to the conventional counterpart in terms of the probability of ruin.
Reviewer 2 Report
Overall comments:
The introduction should be re-written. It provides too much detail, while leaving out details about the paper.
I struggled with the paper. I do not feel the authors set the stage very well in the beginning of the paper. There was a lot of detail that was hard to follow and no clear hypothesis. The authors need to be far clearer up front what they hope to accomplish from the paper.
I also found the math hard to follow, particularly since it was hard to follow the terms used. I also found the English to need substantial work, which detracted from understanding the paper.
Key comments
Paragraph starting with Similar on line 38 should be re-written. There is a lots of detail with no apparent reason or direction. Sentence on line 87 that starts with the second option needs to be rewritten, as you should define Qard-Hasan here. Figures 3 through 6 should be written about. The paragraphs proceeding the figures would be far more effective in communicating your point. The causal reason as to why the Quad hasan loan is preferable is unclear. This is a key part of the paper.
Other more minor comments and edits.
Shorten the first paragraph but taking out a sentence or two. Line 28 , should be uncertainty products – add an s to product\ Rewrite sentence starting on line 35 that starts with “The Takaful operator needs to consider” Line 39 – model should be plural Line 88 – should read, as mentioned. Line 89 should be receive Line 93 should be define Line 94 should be make a repayment Sentence on line 97 starting with the Islamic Financial Services should be re-written as it does not make sense. Should be assets on line 108. Line 130 should be scholars. Line 138 should be scholars – should cite a few, otherwise, it’s a meaningless comment. Line 148, should be dividends Should table the variables in some way, such as,
|
Variables |
|
|
L1 |
Minimum level of acceptable surplus |
|
L2 |
Trigger point for investment activity |
|
L3 |
Trigger point for dividends to be shared |
|
Ut |
the participants’ surplus level at the end of the time interval |
|
T |
Surplus level below T |
Define what equation 12 is and what it tells us.
