Adaptation of the Kelly Criterion for High-Frequency Risk Management

The classic Kelly criterion is the benchmark for geometric capital growth, defining the transaction size for each step as a function of the probability of success and the yield ratio. The main assumption of the original theory is environment stationarity. In real-world high-frequency systems, probabilities continuously fluctuate, and transaction execution delays cause the actual entry point to drift relative to the calculated one.

To compensate for these factors, a fractional Kelly criterion is applied. Introducing a reduction coefficient (typically between 0.1 and 0.5) significantly dampens the variance of the balance trajectory while sacrificing only a small portion of long-term growth velocity. Fractional Kelly acts as a risk buffer, protecting the system from sequences of false signals during sudden shifts in expectation.

Integrating adaptive probability estimation using sliding Bayesian filters allows the formula to dynamically scale the allocated capital in real-time. If the uncertainty of the current variance estimate exceeds a critical threshold, the algorithm automatically reduces participation to a minimum, preventing drawdowns during phases of instability.