Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments
The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can res...
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| Language: | English |
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/2076-3417/15/13/7143 |
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| author | Bartłomiej Gaweł Bogdan Rębiasz Andrzej Paliński |
| author_facet | Bartłomiej Gaweł Bogdan Rębiasz Andrzej Paliński |
| author_sort | Bartłomiej Gaweł |
| collection | DOAJ |
| description | The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can result in undervaluing the future opportunities and risks. Our contribution is built around a correlated random–fuzzy Geometric Brownian Motion, a hybrid Monte Carlo engine that propagates mixed uncertainty into a probability box, combined with three p-box-to-CDF transformations (pignistic, ambiguity-based and credibility-based) to reflect decision-maker attitudes. Our approach utilizes the Datar–Mathews method (DM method) to gather relevant information regarding the potential value of a real option. By combining probabilistic and possibilistic approaches, the proposed valuation model incorporates hybrid Monte Carlo simulation and a random–fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision maker’s attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options. |
| format | Article |
| id | doaj-art-94e1c6aa7cd04674b45961cb1a2224ed |
| institution | Matheson Library |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-94e1c6aa7cd04674b45961cb1a2224ed2025-07-11T14:35:50ZengMDPI AGApplied Sciences2076-34172025-06-011513714310.3390/app15137143Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain EnvironmentsBartłomiej Gaweł0Bogdan Rębiasz1Andrzej Paliński2Faculty of Management, AGH University, 30-059 Kraków, PolandFaculty of Management, AGH University, 30-059 Kraków, PolandFaculty of Management, AGH University, 30-059 Kraków, PolandThe article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can result in undervaluing the future opportunities and risks. Our contribution is built around a correlated random–fuzzy Geometric Brownian Motion, a hybrid Monte Carlo engine that propagates mixed uncertainty into a probability box, combined with three p-box-to-CDF transformations (pignistic, ambiguity-based and credibility-based) to reflect decision-maker attitudes. Our approach utilizes the Datar–Mathews method (DM method) to gather relevant information regarding the potential value of a real option. By combining probabilistic and possibilistic approaches, the proposed valuation model incorporates hybrid Monte Carlo simulation and a random–fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision maker’s attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options.https://www.mdpi.com/2076-3417/15/13/7143real optionsDatar–Mathews methodpossibility theoryinvestment decisionhybrid Monte Carlo simulation |
| spellingShingle | Bartłomiej Gaweł Bogdan Rębiasz Andrzej Paliński Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments Applied Sciences real options Datar–Mathews method possibility theory investment decision hybrid Monte Carlo simulation |
| title | Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments |
| title_full | Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments |
| title_fullStr | Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments |
| title_full_unstemmed | Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments |
| title_short | Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments |
| title_sort | integrating probability and possibility theory a novel approach to valuing real options in uncertain environments |
| topic | real options Datar–Mathews method possibility theory investment decision hybrid Monte Carlo simulation |
| url | https://www.mdpi.com/2076-3417/15/13/7143 |
| work_keys_str_mv | AT bartłomiejgaweł integratingprobabilityandpossibilitytheoryanovelapproachtovaluingrealoptionsinuncertainenvironments AT bogdanrebiasz integratingprobabilityandpossibilitytheoryanovelapproachtovaluingrealoptionsinuncertainenvironments AT andrzejpalinski integratingprobabilityandpossibilitytheoryanovelapproachtovaluingrealoptionsinuncertainenvironments |