This work develops a structural framework for analysing a broad class of sequential stochastic decision systems. Many real-world decision environments share a common structure: opportunities arise over time, agents must decide whether to act on them, and outcomes are asymmetric between gains and losses. Examples include systematic trading strategies, diagnostic screening programs, hiring pipelines, and classical betting problems. The paper shows that within the natural model class of compound Poisson reward processes with Bernoulli payoffs, such systems can be described using a minimal parameter triple: λ – opportunity arrival intensity p – decision (classifier) accuracy κ = μ⁺/μ⁻ – payoff asymmetry These correspond to three independent mechanisms governing system performance: opportunity generation, decision reliability, and reward asymmetry. The main theoretical results establish that this parameter triple forms a minimal structural parameterisation of the model class. Specifically: The representation is sufficient: every admissible triple (λ, p, κ) generates a process in the model family. It is necessary: no two-parameter representation can describe the full family. The parameters are identifiable from the observable distribution of the reward process. The Fisher information matrix is diagonal, implying statistical orthogonality between the parameters. The framework also yields a simple admissibility condition p (κ+1) >1p (+1) > 1p (κ+1) >1, which partitions the parameter space into qualitatively distinct regimes corresponding to different failure modes of sequential decision systems. As a worked example, the paper analyses the well-known Kelly betting problem, showing that the commonly cited approximation f0≈2f∗f₀ 2f^*f0≈2f∗ for the ruin boundary arises as a second-order Taylor expansion and fails in regimes of large payoff asymmetry. The framework provides a unified way to interpret this failure as a transition between parameter regimes. Beyond this example, the parameterisation offers a compact diagnostic language for analysing sequential decision environments across different domains. The paper emphasises that the underlying components—compound Poisson processes, Wald’s identity, Fisher information, and the Kelly criterion—are classical; the contribution lies in their joint structural formulation and analysis within a single minimal framework.
Subhodeep Saha (Sun,) studied this question.