PONE-D-23-41707Equilibrium Strategy In A Defined Benefit Pension Plan With Community Pension ModelPLOS ONE

Dear Dr. Tian,

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Academic Editor

PLOS ONE

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Additional Editor Comments:

Reviewer-1

General comments

This paper studies the equilibrium strategy for a defined benefit pension plan with

community pension model. The authors establish a stochastic differential game model

of pension under community pension, and using the Hamilton-Jacobi-Bellman equation,

obtain the Markov perfect Nash equilibrium strategy. Finally, a numerical illustration

shows the influence of different risk aversion on the equilibrium strategy.

Overall, this paper’s language expression is poor, the logic is not particularly clear,

there are few and outdated literature used, and there are also formatting issues. In short,

this work is somewhat rough.

Specific comments

• Page 3, multiple spaces in line 57, and fewer spaces in line 64. Similar issues also exist in other pages.

• Page 3, What does the symbol “t” refer to and is there a range of it?

• Page 5, “C(t)” in equation (5) is the contribution amount, not the contribution rate.

• It is necessary to explain the meaning of the symbol γ” in Page 6 line 119 and “δ” in Page 6 line 120.

• The definition of equilibrium strategy, and the verification theorem for solutions are not mentioned in this paper.

• Proposition 3.1 in Page 7, how the statement “the constants A and B mentioned in equations (8) and (9) can be determined constant A is negative and constant B is positive“ obtain?

• Page 8, how the HJB equations obtain in lines 153-155?

• Page 10 line 191, how “0.8“ obtain?

• In Fig 1, the proportion of investment in risky assets increases with the increase of the risk aversion, this is not in line with the actual investment situation.

• The reference is scarce and outdated

Reviewer-2

PONE-D-23-41707

1. In the present manuscript, the authors analyze an equilibrium strategy for a defined benefit plan with a community pension model by employing the Hamilton-Jacobi-Bellman equation. The authors determined the Markov-perfect Nash equilibrium solution by optimizing the portfolios and yielding the risk tolerance. The study is good in terms of correlating the unfunded actuarial liability and the supplemental contribution rate; however, it needs several clarifications, which should be added before the final consideration of the manuscript.

2. The authors need to elaborate on the advantages of the model used in this study over others.

3. Additionally, it would be better if the authors could underline the limitations of this study that need further study (as suggested in the conclusion section).

4. The captions of all the figures are not defined in such a manner that the readers could get the idea by going through the figure alone. Hence, all the experimental conditions and considerations should be given in a descriptive manner.

5. The conclusion section is a weak point. The authors should highlight the findings of their study, including some numerical values.

6. The English language of the manuscript thoroughly needs revision for better readability. The authors should pay attention in this direction.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: No

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

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Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

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Reviewer #1: No

Reviewer #2: No

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Specific comments

• Page 3, multiple spaces in line 57, and fewer spaces in line 64. Similar issues also exist in other pages.

• Page 3, What does the symbol “t” refer to and is there a range of it?

• Page 5, “C(t)” in equation (5) is the contribution amount, not the contribution rate.

• It is necessary to explain the meaning of the symbol γ” in Page 6 line 119 and “δ” in Page 6 line 120.

• The definition of equilibrium strategy, and the verification theorem for solutions are not mentioned in this paper.

• Proposition 3.1 in Page 7, how the statement “the constants A and B mentioned in equations (8) and (9) can be determined constant A is negative and constant B is positive“ obtain?

• Page 8, how the HJB equations obtain in lines 153-155?

• Page 10 line 191, how “0.8“ obtain?

• In Fig 1, the proportion of investment in risky assets increases with the increase of the risk aversion, this is not in line with the actual investment situation.

• The reference is scarce and outdated.

Reviewer #2: PONE-D-23-41707

1. In the present manuscript, the authors analyze an equilibrium strategy for a defined benefit plan with a community pension model by employing the Hamilton-Jacobi-Bellman equation. The authors determined the Markov-perfect Nash equilibrium solution by optimizing the portfolios and yielding the risk tolerance. The study is good in terms of correlating the unfunded actuarial liability and the supplemental contribution rate; however, it needs several clarifications, which should be added before the final consideration of the manuscript.

2. The authors need to elaborate on the advantages of the model used in this study over others.

3. Additionally, it would be better if the authors could underline the limitations of this study that need further study (as suggested in the conclusion section).

4. The captions of all the figures are not defined in such a manner that the readers could get the idea by going through the figure alone. Hence, all the experimental conditions and considerations should be given in a descriptive manner.

5. The conclusion section is a weak point. The authors should highlight the findings of their study, including some numerical values.

6. The English language of the manuscript thoroughly needs revision for better readability. The authors should pay attention in this direction.

**********

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Reviewer #1: No

Reviewer #2: No

**********

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Attachments

Attachment

Submitted filename: Report on Pone.pdf

Optimal Tactics in Community Pension Model for Defined Benefit Pension Plans

PONE-D-23-41707R1

Dear Dr. Tian Tian,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Sadia Ilyas, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

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