FINANCIAL CALCULATIONS AND MODELLING FOR BUDGETING, FORECASTING, AND RISK ASSESSMENT.

Abstract

True economic choice involves accurate budgeting, reliable forecasting, and strong risk assessment. This paper presents an integrated mathematical framework that combines deterministic optimization and stochastic modeling with time series forecasting to improve planning accuracy. The budget component treats the allocation of scarce project resources among various competing projects as a constrained linear optimization model designed to minimize the variance of the overall cost. We use an autoregressive integrated moving-average (ARIMA) approach with seasonal adjustments to forecast revenue and expenditure trends. Using Monte Carlo-based stochastic simulation, risk assessment quantifies the probability distribution of different losses and the Value-at-Risk for any market scenario. The proposed models utilize simulated financial data and a real-world case study to demonstrate improved forecast accuracy and more effective uncertainty management compared to traditional spreadsheet methods. This framework provides organizations with a scalable, data-driven approach to budgeting and proactive risk management.