  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.
