Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear author,

Thank you for giving me the opportunity to read this article. I think you tackle a very novel approach to real options. The theory has been around for a number of years, but recent developments in how uncertainty is taken into account do have implications for RO valuation. However, before moving toward publication, I would suggest some improvements. Two elements seem to be missing:

A. Comparative Evaluation
I believe your article would gain in richness and appeal if you presented a better-structured table comparing the different techniques used to evaluate real options. You might also consider the supplementary material proposed in the following article you cited:
Walters, D. J., Ülkümen, G., Tannenbaum, D., Erner, C., & Fox, C. R. (2023). Investor behavior under epistemic vs. aleatory uncertainty. Management Science, 69(5), 2761–2777. https://doi.org/10.1287/mnsc.2022.4489

It could also make sense to briefly discuss the evolution of uncertainty representation, in contrast with what I believe was the pioneering book on this topic in real options: Investment under Uncertainty, by Dixit and Pindyck, Princeton University Press, 1994.

B. Managerial Insights
The managerial insights are almost absent. I believe it would be valuable to increase the discussion in the conclusion around these points. For example, by opening the reflection to other forms of options, such as when companies are competing by option. See for example:

• Burger-Helmchen, T. (2009). Option chain and change management: A structural equation application. European Management Journal, 27(3), 176–186.

• Čirjevskis, A. (2024). Exploring the Usefulness of Real Options Theory for Foreign Affiliate Divestments: Real Abandonment Options’ Applications. Journal of Risk and Financial Management, 17, 438. https://doi.org/10.3390/jrfm17100438

I hope these small elements help to improve your work.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

see the attachment.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors of the paper "Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments " present a new method for evaluating investment projects in uncertain conditions, which utilizes the Datar-Mathews Method and a combination of probabilistic and possibilistic approaches. To demonstrate the effectiveness of the developed approach, a numerical illustration is presented. The developed approach looks interesting and may be relevant to the journal's audience. However, the reviewer recommends revising the manuscript to address the following concerns:

1. The contribution should be assessed in light of the state of the art and other approaches published in the literature on real options valuation.
2. Building on the previous point, the manuscript should elaborate on the practical advantages of the developed approach and its competitiveness, particularly in comparison to the Black-Scholes-based approaches.
3. It is recommended that the notation be reviewed throughout the manuscript to ensure consistency. Additionally, a table summarizing the nomenclature, including all parameters, sets, and variables, should be added for clarity.
4. The equations lack sufficient detail and should be accompanied by comprehensive explanations to demonstrate the added value of the proposed approach. Additionally, a flowchart is recommended to illustrate the steps involved.
5. Fig.3-Fig. 5 should incorporate an economic and financial interpretation of how the uncertainty range of the Net Present Value influences investment decisions.
6. The conclusion section should be concise, highlighting the main contribution, competitiveness, and practical value of the developed approach. In this regard, I recommend including a discussion section that summarizes the research's key findings.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper proposes a novel hybrid approach integrating probability and possibility theory, which evaluates real option values in uncertain environments by combining the Datar-Mathews method, hybrid Monte Carlo simulation, and random-fuzzy Geometric Brownian Motion while considering parameter interdependence, and validates through a case study that it can more accurately integrate subjective and objective information to support investment decisions. However, the paper still has the following shortcomings:

1. The setting of fuzzy numbers is relatively subjective, and an expert calibration mechanism should be added to reduce arbitrariness;
2. The economic implications of the interval regression coefficients for parameter interdependence need further explanation;
3. The applicable boundaries of the decision-theoretic foundation for p-box transformation are not clarified;
4. The sensitivity analysis on the impact of changes in the range of fuzzy numbers on the width of the NPV p-box in the case study needs to be supplemented;
5. The performance comparison with FROV lacks direct case verification;
6. The abstract does not clearly state the core formulas or model names in advance, and the conclusion is not explicit enough about the methodological universality;
7. There are minor issues such as skipped formula numbering and missing key data units in chart titles.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

The proposed manuscript entitled “Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments” explores how to evaluate projects under uncertain conditions. Specifically, this study focuses on two types of uncertainty, the aleatory and the epistemic uncertainty, and takes into account both probabilistic and possibilistic methods to evaluate the final outcome of projects using a hybrid approach of Monte-Carlo simulation and random-fuzzy methods.

The manuscript addresses a critical and challenging issue in decision-making under uncertainty. The comments from the 1^st review round were addressed properly and, from my perspective, the manuscript can be published in its present form.

Kind regards.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

The authors have addressed the suggestions from the first review and indicated the places of these changes within the manuscript. The revised manuscript demonstrates significant improvement. 

Reviewer 4 Report

Comments and Suggestions for Authors

This paper presents a well - structured and innovative study on investment analysis, contributing significantly to the field. The research methodology is rigorous, and the data analysis is comprehensive, effectively supporting the conclusions. The writing is clear and adheres to academic standards. Minor improvements are suggested: such as minor grammar errors, et al. Once these are addressed, the manuscript is ready for acceptance.