Optimal Bounds and Practical Insights: Cantelli’s Inequality Revisited

Abstract

[Abstract:] In this paper, we establish three upper bounds of Cantelli’s inequality type, out of which two are optimal, improving upon previous results, including those derived from Cantelli’s and Hoeffding’s inequalities. We demonstrate the practical relevance of our research by analyzing exchange-rate risk in the real estate market. Specifically, we develop an effective hedging strategy that enables firms to safeguard their profits in the case of currency mismatches between revenue and costs. By effectively modeling the dependence structure of revenue and costs, we enhance the precision of our bounds, as demonstrated through simulation data.