On Generalizations of Tchebychef's Inequality

Satisfying Bank Capital Requirements: A Robustness Approach in a Modified Roy Safety-First Framework

This study considers an asset-liability optimization model based on constraint robustnesswith the chance constraint of capital to risk assets ratio in a safety-first framework under the conditionthat only moment information is known. This paper aims to extend the proposed single-objectivecapital to risk assets ratio chance constrained optimization model in the literature by considering themulti-objective constraint robustness approach in a modified safety-first framework. To solve theoptimization model, we develop a deterministic convex counterpart of the capital to risk assets ratiorobust probability constraint. In a consolidated risk measure of variance and safety-first framework,the proposed distributionally-robust capital to risk asset ratio chance-constrained optimization modelguarantees banks will meet the capital requirements of Basel III with a likelihood of 95% irrespectiveof changes in the future market value of assets. Even under the worst-case scenario, i.e., when loansdefault, our proposed capital to risk asset ratio chance-constrained optimization model meets theminimum total requirements of Basel III. The practical implications of the findings of this study arethat the model, when applied, will provide safety against extreme losses while maximizing returnsand minimizing risk, which is prudent in this post-financial crisis regime.