Abstract
In this paper, we introduce two new types of conditional random set taking values in a Banach space: the conditional interior and the conditional closure. The conditional interior is a version of the conditional core, as introduced by A. Truffert and recently developed by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure is a generalization of the notion of conditional support of a random variable. These concepts are useful for applications in mathematical finance and conditional optimization.
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Notes
E. Lépinette apologizes to A. Truffert for not having quoted her paper [4].
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Acknowledgements
Emmanuel Lépinette thanks Institut Louis Bachelier for the financial participation in the organization of the yearly Bachelier Colloquium at Metabief, France. Meriam El Mansour thanks the mathematical department Ceremade, Paris Dauphine University, for the financial participation allowing her to reside and work in the laboratory.
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Communicated by Michel Théra.
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El Mansour, M., Lépinette, E. Conditional Interior and Conditional Closure of Random Sets. J Optim Theory Appl 187, 356–369 (2020). https://doi.org/10.1007/s10957-020-01768-w
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DOI: https://doi.org/10.1007/s10957-020-01768-w
Keywords
- Conditional random set
- Conditional optimization
- Super-hedging problem
- European option
- Mathematical finance