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- W3201204401 abstract "In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump frequencies and magnitudes, namely, the Levy density, is of critical importance. A specific obstacle to carrying out model-based (e.g., Bayesian) inference in such problems is that, for general Levy processes, the likelihood is intractable. To overcome this obstacle, here we adopt a Gibbs posterior framework that updates a prior distribution using a suitable loss function instead of a likelihood. We establish asymptotic posterior concentration rates for the proposed Gibbs posterior. In particular, in the most interesting and practically relevant case, we give conditions under which the Gibbs posterior concentrates at (nearly) the minimax optimal rate, adaptive to the unknown smoothness of the true Levy density." @default.
- W3201204401 created "2021-09-27" @default.
- W3201204401 creator A5056053058 @default.
- W3201204401 creator A5081850677 @default.
- W3201204401 date "2021-09-14" @default.
- W3201204401 modified "2023-09-27" @default.
- W3201204401 title "Gibbs posterior inference on a Levy density under discrete sampling" @default.
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- W3201204401 doi "https://doi.org/10.48550/arxiv.2109.06567" @default.
- W3201204401 hasPublicationYear "2021" @default.
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