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Stochastic partial differential equations with coefficients depending on VaR
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Pak, Alexey (2017) Stochastic partial differential equations with coefficients depending on VaR. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3104120~S15
Abstract
In this paper we prove the well-posedness for a stochastic partial differential equation (SPDE) whose solution is a probability-measure-valued process. We allow the coefficients to depend on the median or, more generally, on the γ-quantile (or some its useful extensions) of the underlying distribution. Such SPDEs arise in many applications, for example, in auction system described in [2]. The well-posedness of this SPDE does not follow by standard arguments because the γ-quantile is not a continuous function on the space of probability measures equipped with the weak convergence.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Business mathematics, Finance -- Mathematical models, Capital assets pricing model | ||||
Official Date: | May 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich) | ||||
Format of File: | |||||
Extent: | 96 leaves : illustrations | ||||
Language: | eng |
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