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A Stochastic Process Perspective on Hybrid Log-Normal and Machine Learning Models for Financial Risk under Left-Censored Data | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 1، اردیبهشت 2026، صفحه 159-190 اصل مقاله (745.96 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.87190.1201 | ||
| نویسندگان | ||
| Tahar Mohamed Boukadoum* 1؛ Kamel Boukhetala2 | ||
| 1university of science USTHB. department of probability and statistics . laboratory of stochastic modeling and data mining | ||
| 2university of science USTHB. department of probability and statistics. Laboratory of stochastic modeling and data mining | ||
| چکیده | ||
| In the context of financial risk management, predictive modeling under censored data remains a complex challenge. This paper develops and compares two approaches: a traditional log-normal regression model and a hybrid framework combining log-normal regression with an XGBoost-based correction layer. While the parametric component captures the structured relationships between covariates and claim costs, the machine learning layer adjusts for nonlinear residual structure. Building on this, we introduce a stochastic interpretation of the hybrid estimator by modeling prediction errors as a Gaussian process. We derive a formal variance decomposition, separating model-based and correction-layer uncertainty. To quantify this, we implement both simulation-based estimation and diagnostic tools for residual stationarity and ergodicity. Additionally, we propose a Bayesian stochastic extension by placing priors over model parameters and deriving posterior predictive intervals. A novel contribution of this work is the incorporation of residual dynamics via autoregressive stochastic processes, where residuals from the hybrid model are modeled as AR(1) processes and also as a Diffusion Process. This allows for modeling temporal dependence and improves interpretability of correction structures. | ||
| کلیدواژهها | ||
| log-normal regression؛ Hybrid model؛ Hybrid estimator؛ censored؛ stochastic process؛ Value at Risk | ||
| مراجع | ||
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