Modeling Volatility of Disaster-Affected Populations: A Non-Homogeneous Geometric-Skew Brownian Motion Approach

Abstract: 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.