Dynamic Population Expectation Theory (DPET)

Dynamic Population Expectation Theory (DPET)

Intro paragraph

Dynamic Population Expectation Theory (DPET) studies how expected value (EV) evolves dynamically in finite non-replacement sampling systems.

Contrary to classical static expectation assumptions, DPET demonstrates that the true expectation at each sampling step is time-dependent and can exhibit systematic positive deviations.

Core formulation section

At sampling step t, the dynamic expectation is defined as:

μt=K−sN−t\mu_t = \frac{K – s}{N – t}μt​=N−tK−s​

where N is the population size, K the number of favorable outcomes, t the number of draws, and s the number of observed successes.

The deviation from static expectation is given by:

Dt=μt−μstaticD_t = \mu_t – \mu_{static}Dt​=μt​−μstatic​

This deviation forms the theoretical basis for exploitable advantages in finite sampling environments.

Validation summary

DPET is primarily validated through:

• Cryptocurrency order book optimization, demonstrating significant reduction in execution slippage
• Baccarat, serving as a classical finite sampling benchmark
• Reinforcement learning, where DPET improves sampling efficiency under non-independent conditions

Scope & impact

DPET extends beyond financial markets to broader domains including operations research, healthcare systems, and game theory.

By relaxing the static expectation assumption, DPET offers a new analytical lens for sequential decision-making under finite resources.

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