This paper delves into the impact of natural disasters on affected populations and underscores the imperative of reducing disaster-related fatalities through proactive strategies. On average, approximately 45,000 individuals succumb annually to natural disasters amid a surge in economic losses. The paper explores catastrophe models for loss projection, emphasizes the necessity of evaluating volatility in disaster risk, and introduces an innovative model that integrates historical data, addresses data skewness, and accommodates temporal dependencies to forecast shifts in mortality. To this end, we introduce a time-varying skew Brownian motion model, for which we provide proof of the solution's existence and uniqueness. In this model, parameters change over time, and past occurrences are integrated via volatility.

翻译：本文深入探讨自然灾害对受影响人口的影响，并强调通过积极策略减少灾害相关死亡人数的必要性。平均每年约有4.5万人死于自然灾害，同时经济损失持续攀升。本文研究了用于损失预测的灾害模型，强调了评估灾害风险波动性的必要性，并引入了一种创新模型，该模型整合历史数据、处理数据偏态性并考虑时间依赖性，以预测死亡率变化。为此，我们提出了一种时变偏斜布朗运动模型，并证明了该模型解的存在性与唯一性。在该模型中，参数随时间变化，并通过波动性整合历史事件。