A multi-period regret decomposition produces an observable statistic whose sign classifies linear algo strategies as liquidity consumers or providers and equals strategy size times squared Roll spread under AR(1) costs, implying N-squared welfare loss from liquidity imbalance.
http://www.nber.org/papers/w35153
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Derives an exact decomposition of cumulative regret into per-period covariances for dynamic policies under i.i.d. costs and unbiased Markov policies, with extensions to non-stationary cases and RL connections.
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Liquidity-Based Audit of Algorithmic Trading Strategies
A multi-period regret decomposition produces an observable statistic whose sign classifies linear algo strategies as liquidity consumers or providers and equals strategy size times squared Roll spread under AR(1) costs, implying N-squared welfare loss from liquidity imbalance.
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Evaluating AI Investment Strategies
Derives an exact decomposition of cumulative regret into per-period covariances for dynamic policies under i.i.d. costs and unbiased Markov policies, with extensions to non-stationary cases and RL connections.