Research on Branching Signature Models
The paper proposes a branching signature model that generalizes the classical geometric rough path based on the branching rough path framework, proving its universal approximation theorem, which can approximate high-level signatures through iterative combinations of low-level signature mappings. The model can explicitly extend the original path to a high-dimensional space via the mapping Ψ, implementing it as the classical geometric signature of the extended path, and its effectiveness is verified in two applications: rough volatility calibration and optimal execution.
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