Analytical Formulas for Risk Assessment for a Class of Problems where Risk Depends on Three Interrelated Variables

Abstract

We derive general analytical formulas for assessing risks in a problem domain where the risk depends on three interrelated variables. More specifically, we derive general analytical formulas for propagating beliefs in a network where three binary variables, A, B and C, are related to a fourth binary variable Z through an ‘AND’ relationship. In addition, we assume that variables A, B and C are interrelated in that a change in one variable may affect the value of each of the other two. The analytical formulas derived in this article determine the overall belief and plausibility that Z is true or not true, given that we have beliefs on variables A, B and/or C. To demonstrate the importance of the general results, we use the results to develop models applicable to three real-world situations. The first model can aid external auditors in assessing the quality of an audit client’s internal audit function to determine the extent to which the internal auditor’s work can be relied on in the conduct of a financial audit while the second can aid in assessing the risk of impaired auditor independence when conducting a financial statement audit. The third model can be used to assess the risk of management fraud in financial reporting. Assessment of such risks is of critical importance to external auditors, regulators, and the investing public. Analytical formulas to help address these types of important business and economic problems have not been available prior to these derivations.