Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

Round 1

Reviewer 1 Report

The paper introduces a analytical formulas for conditional moments of inhomogeneous nonlinear drift constant elasticity of variance process, without having a condition on eigenfunctions or the transition PDF . The analytical results are examined through the Monte Carlo simulations for a specific parameters.

The analytical solutions are correct and it adds significant contribution to the literature. 

It would be good to see a section on applications of these results. Moreover, the authors could highlight the usefulness  and flexibility of the assumptions 1 and 2, which is core to the entire analysis.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

A file with the report is attached.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Report on the manuscript "symmetry-1776831" entitled "Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift CEV Process"

 

This manuscript studies an inhomogeneous nonlinear drift constant elasticity of variance process. Random fluctuations with an asymmetric standard Brownian motion are considered. Experimental results are provided. Conclusions about this investigation are reported.

 

I have a good opinion about this work, which is relatively well written, its topic should be of interest for Symmetry, and its results are a suitable complement to the existing works. However, I think several aspects must be improved before it is suitable for publication, which I detail next.

 

1. The title of the manuscript needs to be rethought. Abbreviations must be avoided in a title.

 

2. The manuscript needs to be proofread by the authors. I have noted some drafting problems.

 

3. Words in the title are not usually in the keywords. In addition, the keywords are often written in alphabetical order. Please avoid using general keywords such as "closed-form formulas".

 

4. The authors must check the use of all acronyms, abbreviations, and notations employed in the whole manuscript. Please define all the acronyms and abbreviations and then use them. Remember that the abstract is independent of the body of the paper, so that acronyms/abbreviations defined in the abstract (that are used there) must be again defined in the body of the paper. Please move the summary of abbreviations located at the end of the paper to the beginning. 

 

5. Some notations must be written in text style and not math style. Just as an example, please change "d" for differentials to "\textrm{d}" (in LaTeX code) to differentiate it from a possible math variable "d" and similarly with "e" for the exponential function used, for example, in Eq. (6). In this equation and the whole paper, please change the differential used in the integral as indicated above.

 

6. Fractions used in a line of text must be written with "/" instead of using "<\frac" (in Latex code); see, for example, Assumption 1. Please check it in the whole manuscript. I found several of them.

 

7. Please add a brief introduction to Sections 2, 3, and 6, at the beginning, such you did with Sections 4 and 5.

 

8. The introduction must be improved, presenting the problem from the more general to the most specific, including the bibliographical review, which must be enhanced. This section must finish (no before) by stating the problem being analyzed in this study, indicating, "Therefore, to the best of our knowledge, there are no studies that...". Then, the authors must state the objectives of their study, and in the following paragraph (such as this is now), the description of the sections of the paper must be mentioned.

 

9. Is this manuscript applying known methods to a real problem, or a new methodology is developed? This must be clearly stated.

 

10. The authors must provide more details about the computational framework employed in the manuscript. For example, software and packages utilized, features of the computer employed, runtimes, and other computational aspects must be added. 

 

11. The authors must summarize their methodology into an algorithm and/or in a flowchart so that the readers can follow it easier. Thus, the practitioners could have some guidelines when applying this methodology.

 

12. I do not have each numerical result in detail. I recommend the authors to check them.

 

13. In my opinion, the implications and results of the study are underdeveloped and must be improved and explained further in the final section.

 

14. Also, the authors must add limitations of the study and ideas for further research. Then, I suggest titling the final section: "Conclusions, limitations, and future research".

 

15. The authors must check whether all references are cited and all citations are in the reference list.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

A file with the report is attached.

Comments for author File: Comments.pdf

Reviewer 3 Report

I am satisfied with the authors' revision. Therefore, I am pleased to recommend acceptance of this article in its present form.