Abstract
Referring to Dempster-Shafer theory, we introduce a bivariate random walk enforcing Markovianity and time-homogeneity under a pessimistic view towards ambiguity. This is done through a suitable family of joint t-step transition belief functions, generalizing the product of two independent binomial transition probabilities, where ambiguity is expressed by a parameter. Given a real-valued function of the pair at a fixed time horizon, we define the dynamic lower and upper Value-at-Risk (VaR), generated by the corresponding dynamic p-box.
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Acknowledgement
We acknowledge the support of the PRIN 2022 project “Models for dynamic reasoning under partial knowledge to make interpretable decisions” (Project number: 2022AP3B3B, CUP Master: J53D23004340006, CUP: B53D23009860006) funded by the European Union - Next Generation EU (Missione 4 Componente 2). The first and third authors have been supported by the Sapienza University of Rome research project “Ambiguity: its role in asset pricing and insurance” (Grant number: RM123188F744909D).
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Cinfrignini, A., Petturiti, D., Vantaggi, B. (2025). Imprecise Dynamic Value-at-Risk Induced by a DS-Bivariate Random Walk. In: Destercke, S., Martinez, M.V., Sanfilippo, G. (eds) Scalable Uncertainty Management. SUM 2024. Lecture Notes in Computer Science(), vol 15350. Springer, Cham. https://doi.org/10.1007/978-3-031-76235-2_9
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