Price manipulation in nonlinear transient impact models: rigidity before memory and complete positivity after memory

Minhyeok Lee

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Abstract: Transient impact models compose a nonlinearity with a memory kernel, and the order of composition determines the criterion for absence of price manipulation. We classify both orders. If an arbitrary instantaneous law $f$ acts on the trading rate before any nonzero integrable Volterra kernel, nonnegative cost on every finite piecewise-constant round trip forces $f$ to be affine, and linear for every nonzero convolution kernel. In particular, the power law $\mathrm{sgn}(x)|x|^\delta$, $\delta>0$, combined with power-law decay $t^{-\gamma}$, $0

Date: 2026-09
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