Exploratory Dividend Optimization with Entropy Regularization
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis article proposes an investigation into the dividend optimization problem within the entropy regularization framework, employing a continuous-time reinforcement learning approach. The abstract, introduction, and literature review are meticulously crafted and exhibit a high level of academic rigor. However, the definition and articulation of the research objective do not stand out clearly throughout the text.
It is recommended that the research objective be explicitly stated in the abstract, reiterated at the conclusion of the introduction, and reintroduced at the beginning of the conclusion to provide a continuous narrative and enhance reader understanding. This adjustment is crucial for guiding the reader cohesively through the paper.
The methodology employed and the analysis of results are presented in a clear and objective manner, reflecting a standard of academic excellence. Nevertheless, it is imperative for the study to strive for more comprehensive conclusions. While some conclusions are presented, it is necessary to explicitly emphasize the impact that this research aims to have on society.
In summary, while the article demonstrates strong academic skills in constructing the abstract, introduction, and literature review, there is an opportunity for improvement in delineating and emphasizing the research objective, as well as in expanding conclusions and contextualizing the expected social impact. This refinement will significantly contribute to a more accessible and comprehensive interpretation of the text.
The bibliography is extensive and current.
Comments on the Quality of English Language
In a scientific text, its quality is very important. The English in your writing seems fine to me, but I admit I'm not a native English speaker.
Author Response
Thanks for your comment. We have revised the abstract, the conclusion of introduction part, and the conclusion part. In particular, we emphasized the research objective, our contribution, and the social impact. From technical point of view, the optimal exploratory solution is a truncated exponential distribution and the value function depends on the choice of exploration weight. In an unknown market environment, insurance companies can achieve long-term optimal dividends by controlling exploration weight.
Reviewer 2 Report
Comments and Suggestions for Authors Thank you for inviting me to review this manuscript, titled “Exploratory Dividend Optimization with Entropy Regularization”. The research addresses the dividend optimization problem in the entropy regularization framework, considering decision in an unknown environment. The research topic proposed by the authors is current and relevant in the field.Please find my detailed comments below:
Regarding the abstract, I suggest that the authors outline the implications of the study.In the introduction, the authors present the scientific context of the research, the aim of the paper and the authors’ contributions. The key idea of the study consists in using distribution as the control to solve the entropy-regularized dividend optimization problem.
The authors approach the classical optimal dividend model and present the exploratory formulation, by taking into consideration the reinforcement learning technique to establish the optimal/near-optimal dividend paying strategy through trial-and-error interactions with the unknown environment. They establish the exploratory HJB equation. For suitable choices of the maximal dividend paying rate and the temperature parameter, the value function of the exploratory dividend optimization problem is significantly different from the value function in the classical dividend optimization problem. The value function of the exploratory dividend optimization problem is classified into three cases based on its monotonicity.
To ensure robustness of the study, the numerical examples of optimal exploratory policy and corresponding value function which solves exploratory HJB equation based on the theoretical results are presented.
The authors clearly show the results. The conclusions are consistent with the evidence and arguments presented and they address the main question posed.
I would suggest a proofreading (e.g. the second sentence of the conclusions).
Thank you for this interesting paper.
Best Regards
Author Response
Thanks for your comment. We have proofread the paper and revised the necessary wordings. We also emphasized our research objective and contribution of this paper in the abstract. Our results suggest that in an unknown market environment, insurance companies can achieve long-term optimal dividends by controlling exploration weight.
