6 problems
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The small-noise quadratic privacy-subsidy conjecture
For an -differentially private channel with Laplace noise, let denote the noise scale and let the privacy-subsidy rate be the subsidy generated by the resultin…
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The linear-quadratic trading conjecture for Kyle's model with stochastic liquidity
In the stochastic-liquidity Kyle model, let the fundamental price be normally distributed, let the informed trader's trading rate denote the rate at which that trader tr…
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Fee mitigation of arbitrage losses for arbitrary CFMM replication
A constant-mean market maker is a particular CFMM, and the paper considers whether fees can mitigate arbitrage losses sufficiently to allow replication without additional initial c…
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Non-uniform priors outperform uniform priors during crises and nonlinear market dynamics
The model assigns agents prior beliefs over possible market conditions, with a uniform prior giving equal probability to all conditions and a non-uniform prior assigning unequal pr…
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Kyle's conjecture on the stability of market depth
Let market depth denote the sensitivity of prices to the total order, so that its reciprocal is the price impact of the total order. Kyle's conjecture. Neither increasing nor decre…
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Time-dependent barrier conjecture for buy and wait regions
Let be a time before the terminal time , let be the number of shares still to be purchased, and let … , or wait for resilience to decrease … --plane is divided by a…