Abstract Dynamic exposure rules can appear effective simply because they reduce risky participation, not because they time exposure well. This study evaluates Pogi, a recursive FULL/PARTIAL/NONE controller that separates portfolio composition from total risky exposure and uses a non-executed shadow path to observe recovery during defensive states. Using daily cryptocurrency data from 2014–2026, eight chronological test folds, recursive transaction costs, and CRRA certainty-equivalent welfare, Pogi is compared with static scaling, volatility targeting, CPPI, drawdown throttling, moving-average control, fractional Kelly scaling, and an exact ex-post exposure-matched diagnostic. The analysis also tests initialization and memory sensitivity, timing nulls, search capacity, selection-aware inference, and external validation using U.S. industry portfolios and frozen cross-market transfer. The completed evaluation did not establish robust welfare superiority for Pogi or support a broader methodological contribution under the pre-specified evidence criteria. The results instead show why dynamic exposure rules should be judged against exposure-matched benchmarks, model-search controls, recursive-state diagnostics, and genuinely external validation.
The Karhunen–Loève (KL) expansion provides an optimal orthogonal series representation of second-order stochastic processes and random fields. This paper presents a complete mathematical formulation of the KL theory using native Office Math Markup Language (OMML) equations, covering the governing Fredholm integral eigenvalue problem, the expansion and its coefficients, truncation error bounds, and the normalized representation. Building upon this theoretical foundation, we systematically explore practical applications of the KL expansion in contemporary supply-chain research themes: quantum-inspired optimization and uncertainty quantification in logistics networks; construction of resilient and adaptive digital twins for global supply chains; stochastic modelling supporting artificial-intelligence and blockchain integration for transparency, traceability and resilience; and uncertainty-aware modelling in sustainable and green logistics. The KL expansion emerges as a rigorous, computationally tractable tool for dimensionality reduction, random-field generation and risk quantification across these domains, thereby bridging classical stochastic process theory with the emerging requirements of Industry 4.0 and quantum-era logistics systems. Keywords— Karhunen–Loève expansion; stochastic processes; uncertainty quantification; digital twin; supply chain resilience; quantum logistics; green logistics; AI–blockchain integration.
Open access
Supply Chain Resilience and Risk Management
Risk and Portfolio Optimization
Infrastructure Resilience and Vulnerability Analysis