Research Article
Probability of Ruin in Finite Time Given by a Variable Memory Hawkes Process in the Univariate Case with Brownian Perturbation
Souleymane Badini*
,
Frederic Bere
Issue:
Volume 10, Issue 3, September 2025
Pages:
41-45
Received:
4 June 2025
Accepted:
18 June 2025
Published:
10 July 2025
Abstract: Our article relates to the field of actuarial science, where the analysis of the probability of ruin is a fundamental issue for insurance companies. The stability of reserves is a key factor in ensuring the sustainability of insurance companies, and understanding the mechanisms that influence this risk allows for the optimization of management strategies. The main objective of this study is to establish an expression to calculate the probability of ruin over a finite time horizon. We use the Hawkes process to model the dynamics of claims arrivals, and we introduce Brownian motion at the level of reserve R(t) to incorporate unexpected variations in compensations. By adopting the assumption that the arrival of claims and their amounts, which follow an exponential distribution, are independent. Then, considering the claims modeled by α-stable distribution. The key ideas developed in this article are based on several aspects: The Hawkes process is used to describe the frequency of claims, taking into account the impact of past events on the future dynamics of losses. A stochastic oscillation (Brownian motion) is integrated into the model to reflect variations in the financial reserve. With the previous elements, a mathematical expression for the probability of ruin in a finite time is formulated to assess the level of risk that a reserve faces over a given period.
Abstract: Our article relates to the field of actuarial science, where the analysis of the probability of ruin is a fundamental issue for insurance companies. The stability of reserves is a key factor in ensuring the sustainability of insurance companies, and understanding the mechanisms that influence this risk allows for the optimization of management stra...
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Research Article
Statistically Aware Optimization for Resource-constrained and Geometrically-rich Data: Nigerian Agricultural Case Study
Issue:
Volume 10, Issue 3, September 2025
Pages:
46-57
Received:
16 September 2025
Accepted:
26 September 2025
Published:
26 November 2025
DOI:
10.11648/j.ijssam.20251003.12
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Abstract: Modern machine learning, fueled by large datasets and complex models, faces a critical tension. The statistical principles underpinning learning (generalization, efficiency, robustness) often clash with the computational realities of optimization, especially in a resource constrained environment or when data exhibits inherent geometric structure. This work addresses the theme "Statistics Meets Optimization" by employing an optimization framework explicitly designed to leverage statistical data properties, particularly group invariances/equivariances common in real world data (e.g., spatial rotations in satellite imagery, temporal shifts in sensor data), to achieve significant gains in sample efficiency and convergence speed. We theoretically derive generalization bounds linking the exploitation of data geometry to reduced sample complexity. Empirically, we demonstrate the efficacy of our method on a challenging real world case study, i.e., on predicting crop yield anomalies in Delta State, Nigeria, using limited, noisy, and spatially heterogeneous satellite and meteorological data. Our optimizer achieved a significant performance with 40% less data compared to adaptive baselines (Adam, RMSProp), highlighting the practical impact of statistically-informed optimization, especially for regions facing data scarcity. This work provides a concrete bridge between statistical theory (data structure, efficiency) and optimization practice (algorithm design, scalability), demonstrating that geometry-aware algorithms can democratize effective ML for resource-limited applications.
Abstract: Modern machine learning, fueled by large datasets and complex models, faces a critical tension. The statistical principles underpinning learning (generalization, efficiency, robustness) often clash with the computational realities of optimization, especially in a resource constrained environment or when data exhibits inherent geometric structure. T...
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