Optimal automation under overdispersed discrete risk: thresholds and hysteresis in a Negative Binomial model

arXiv:2510.05487 · q-fin.CP, stat.ML · Submitted 2025-10-07 · Read on arXiv

q-fin.CP, stat.ML

Submitted: 2025-10-07

Updated: 2026-09-26

Comments: Published in Journal of Industrial and Management Optimization, Volume 22, Issue 5, pp. 2503-2554 (2026)

Journal ref: J. Ind. Manag. Optim. 22(5): 2503-2554 (2026)

DOI: 10.3934/jimo.2026092

License: http://creativecommons.org/licenses/by/4.0/

The gist: Decision-making under clustered uncertainty requires models that accommodate discrete overdispersed risk and endogenous control mechanisms.

Terminology

Abstract

Decision-making under clustered uncertainty requires models that accommodate discrete overdispersed risk and endogenous control mechanisms. Standard approaches often impose equi-dispersion or Gaussian assumptions and treat control as exogenous or binary, limiting structural realism. In this paper, we developed a stochastic optimization framework in which risk follows a dynamic Negative Binomial process with time-varying success probability, generating persistent overdispersion and temporal dependence. A continuous control variable mitigated non-tail and tail exposure under convex implementation and adjustment costs. Analytical results showed that overdispersion reshapes the optimal policy, generating interior solutions, dispersion-dependent thresholds, and regime-dependent hysteresis effects that do not arise under equi-dispersed specifications. Simulation evidence confirms that overdispersion amplifies tail risk and induces nonlinear responses. An empirical analysis using daily S&P 500 index data documents significant overdispersion and persistent clustering. The results provide a structural basis for integrating discrete risk modeling with dynamic operational decisions under uncertainty.

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